<?xml version="1.0" encoding="UTF-8" standalone="no"?><rss xmlns:atom="http://www.w3.org/2005/Atom" xmlns:blogger="http://schemas.google.com/blogger/2008" xmlns:gd="http://schemas.google.com/g/2005" xmlns:georss="http://www.georss.org/georss" xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" xmlns:openSearch="http://a9.com/-/spec/opensearchrss/1.0/" xmlns:thr="http://purl.org/syndication/thread/1.0" version="2.0"><channel><atom:id>tag:blogger.com,1999:blog-7829887098258372846</atom:id><lastBuildDate>Thu, 15 Oct 2026 13:20:21 +0000</lastBuildDate><category>Test Series</category><category>Strength of material mock test</category><category>INTERVIEW</category><category>Strength of Material</category><category>aerodynamics mock test</category><category>Vibration Mock Test</category><category>Aircraft Structure</category><category>Basic</category><category>Fluid Mechanics</category><category>Thermodynamics Mock Test</category><category>Aptitude and Reasoning</category><category>GATE Aerospace Engineering</category><category>GATE2022</category><category>Mock Test</category><category>Previous year papers</category><category>Space dynamics</category><category>Vibration</category><category>aerodynamics</category><category>aircraft propulsion</category><category>flight mechanics</category><category>revision notes</category><title>Aero Gate Topper</title><description></description><link>https://aerogatetopper.blogspot.com/</link><managingEditor>noreply@blogger.com (AERO GATE TOPPER)</managingEditor><generator>Blogger</generator><openSearch:totalResults>45</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><language>en-us</language><itunes:explicit>no</itunes:explicit><itunes:subtitle/><itunes:category text="Education"><itunes:category text="Educational Technology"/></itunes:category><itunes:owner><itunes:email>noreply@blogger.com</itunes:email></itunes:owner><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-2291355792395032504</guid><pubDate>Thu, 29 May 2025 17:10:00 +0000</pubDate><atom:updated>2025-05-31T11:24:15.807+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Basic Performance</title><description>&lt;html lang="en"&gt;

&lt;head&gt;
    &lt;title&gt;Linear Algebra Topic-wise Online Quiz&lt;/title&gt;
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&lt;body&gt;
    &lt;div id="user-info" style="display: block;"&gt;

        &lt;!-- Registration Form --&gt;
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            &lt;h1&gt;Enter Your Details&lt;/h1&gt;
            &lt;input type="hidden" id="TitleQuiz" name="TitleQuiz" value="PERFORMANCE" /&gt;
            &lt;input type="hidden" id="password" name="password" value="Basic Performance" /&gt;
            &lt;label for="name"&gt;Name:&lt;/label&gt;
            &lt;input id="username" name="username" required type="text" pattern="[A-Za-z][A-Za-z0-9 ]*" /&gt;

            &lt;button type="submit" id="submit-user-info"&gt;Next&lt;/button&gt;
        &lt;/form&gt;

    &lt;/div&gt;


    &lt;div id="start-page" style="display: none;"&gt;
        &lt;center&gt;
            &lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;
        &lt;/center&gt;
        &lt;span style='font-weight:bold'&gt;&lt;span style="color: red;"&gt;*Important:&lt;/span&gt; Pressing the Escape key will result in automatic submission of the quiz. Please avoid using it during the attempt.&lt;/span&gt;
        &lt;p&gt;&lt;/p&gt;
        &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
        &lt;p&gt;&lt;/p&gt;
        &lt;ol style="text-align: left;"&gt;
            &lt;li&gt;The total duration of the examination is 60 minutes .&lt;/li&gt;
            &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
            &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
        &lt;/ol&gt;
        &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
        &lt;ol style="text-align: left;"&gt;
            &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
            &lt;ol type="a"&gt;
                &lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;
                &lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;
                &lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;
                &lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
            &lt;/ol&gt;
            &lt;li&gt;
                You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;
        &lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
        &lt;ol style="text-align: left;"&gt;
            &lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
            &lt;ol type="a"&gt;
                &lt;li&gt;To select your answer, click on the button on one of the options&lt;/li&gt;
                &lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;
                &lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;
                &lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next &lt;/b&gt;button&lt;/li&gt;
            &lt;/ol&gt;
            &lt;li&gt;
                Procedure for answering a numerical answer type question:&lt;/li&gt;
            &lt;ol type="a"&gt;
                &lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;
                &lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;
                &lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;
                &lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;
            &lt;/ol&gt;
            &lt;li&gt;
                To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;
        &lt;/ol&gt;
        &lt;ol style="text-align: left;"&gt;
        &lt;/ol&gt;
        &lt;center&gt;&lt;button id="start-button"&gt;Start Quiz&lt;/button&gt;&lt;/center&gt;
    &lt;/div&gt;

    &lt;div class="modal" id="myModal" style="display: none;"&gt;
        &lt;div class="modal-content"&gt;
            &lt;h2&gt;Quiz Submission Confirmation&lt;/h2&gt;
            &lt;p&gt;Do you really want to submit this quiz?&lt;/p&gt;
            &lt;button id="confirmSubmit"&gt;Submit Quiz&lt;/button&gt;
            &lt;button id="cancelSubmit"&gt;Cancel&lt;/button&gt;
        &lt;/div&gt;
    &lt;/div&gt;

    &lt;div class="admodal" id="adModal" style="display: none;"&gt;
        &lt;div class="admodal-content"&gt;
            &lt;p&gt;Your result will be shown here. Please wait 5 seconds.&lt;/p&gt;



            &lt;!-- Close Button (Hidden Initially) --&gt;
            &lt;span class="adclose" id="adClose" style="display: none;"&gt;×&lt;/span&gt;
        &lt;/div&gt;
    &lt;/div&gt;

    &lt;div id="fullscreen-container" style="display: none;"&gt;
        &lt;div id="Title" style="background: lightblue; color: #003366; font-size: 12px; font-weight: bold; padding: 5px;  box-shadow: 0 4px 8px rgba(0,0,0,0.1); margin-bottom: 10px;"&gt;
            &lt;div style="display: flex; justify-content: space-between; align-items: center;"&gt;
                &lt;div style="font-size: 16px;"&gt;&lt;b&gt;AERO GATE TOPPER&lt;/b&gt;&lt;/div&gt;
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            &lt;div class="col-md-8" id="question-container" style="width: 66.666666%; overflow-y: auto; "&gt;

                &lt;div class="question" id="question-1" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Temperature decreases and kinematic viscosity increases"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;Which of the following statements are true as altitude increases in troposphere in ISA &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-1" name="mcq-options1" value="Temperature decreases and kinematic viscosity remains same"&gt;
                            &lt;label for="mcq-option1-1"&gt;Temperature decreases and kinematic viscosity remains same&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-1" name="mcq-options1" value="Temperature increases and dynamic viscosity increases"&gt;
                            &lt;label for="mcq-option2-1"&gt;Temperature increases and dynamic viscosity increases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-1" name="mcq-options1" value="Temperature increases and kinematic viscosity increases"&gt;
                            &lt;label for="mcq-option3-1"&gt;Temperature increases and kinematic viscosity increases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-1" name="mcq-options1" value="Temperature decreases and kinematic viscosity increases"&gt;
                            &lt;label for="mcq-option4-1"&gt;Temperature decreases and kinematic viscosity increases&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-2" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-subject="Basic Performance" data-type="NAT" data-explanation="" data-answer="-" data-max="6" data-min="5" data-precision="1"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;An aircraft is crusing at TAS of 7 m/s under ISA conditions, at an altitude density is 0.763kg/m3 . What is the equivalent airspeed (answer in one decimal)&lt;/p&gt;
                    &lt;input type="number" name="nat-options" id="nat-answer2" placeholder="Enter your answer here"&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-3" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Remains same"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;As altitude increases, the minimum drag &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-3" name="mcq-options3" value="Increases"&gt;
                            &lt;label for="mcq-option1-3"&gt;Increases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-3" name="mcq-options3" value=" Decreases"&gt;
                            &lt;label for="mcq-option2-3"&gt; Decreases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-3" name="mcq-options3" value="Remains same"&gt;
                            &lt;label for="mcq-option3-3"&gt;Remains same&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-3" name="mcq-options3" value="None of the above"&gt;
                            &lt;label for="mcq-option4-3"&gt;None of the above&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-4" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-subject="Basic Performance" data-type="NAT" data-explanation="" data-answer="-" data-max="2760" data-min="2740" data-precision="0"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;The sealevel pressure and temperature are 1.005 bar and 293 K. At unknown altitude in troposphere, the pressure and temperature are 71800 Pa and 263K. find the altitude (in meters) in that location? &lt;/p&gt;
                    &lt;input type="number" name="nat-options" id="nat-answer4" placeholder="Enter your answer here"&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-5" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Unstable"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;The sea level pressure and temperature are 1.005 bar and 293 K. At unknown altitude in troposphere, the pressure and temperature are 71800 Pa and 263 K, is the atmosphere &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-5" name="mcq-options5" value="Unstable"&gt;
                            &lt;label for="mcq-option1-5"&gt;Unstable&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-5" name="mcq-options5" value="Can’t say"&gt;
                            &lt;label for="mcq-option2-5"&gt;Can’t say&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-5" name="mcq-options5" value="Neutral"&gt;
                            &lt;label for="mcq-option3-5"&gt;Neutral&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-5" name="mcq-options5" value="Stable"&gt;
                            &lt;label for="mcq-option4-5"&gt;Stable&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-6" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Vertical speed indicator"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;The rate of climb is measured by &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-6" name="mcq-options6" value="Attitude indicator"&gt;
                            &lt;label for="mcq-option1-6"&gt;Attitude indicator&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-6" name="mcq-options6" value="Vertical speed indicator"&gt;
                            &lt;label for="mcq-option2-6"&gt;Vertical speed indicator&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-6" name="mcq-options6" value="Direction gyro"&gt;
                            &lt;label for="mcq-option3-6"&gt;Direction gyro&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-6" name="mcq-options6" value="Turn coordinator"&gt;
                            &lt;label for="mcq-option4-6"&gt;Turn coordinator&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-7" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-subject="Basic Performance" data-type="NAT" data-explanation="" data-answer="-" data-max="6" data-min="4" data-precision="1"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;An aircraft has $CD = 0.04+0.059CL^2$ , the glide angle that results in maximum range of power off glide is ------------. (answer in one decimal)&lt;/p&gt;
                    &lt;input type="number" name="nat-options" id="nat-answer7" placeholder="Enter your answer here"&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-8" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Increases"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;To maintain steady level flight, as altitude increases velocity should &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-8" name="mcq-options8" value="Increases"&gt;
                            &lt;label for="mcq-option1-8"&gt;Increases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-8" name="mcq-options8" value="None of the above"&gt;
                            &lt;label for="mcq-option2-8"&gt;None of the above&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-8" name="mcq-options8" value="Remains same"&gt;
                            &lt;label for="mcq-option3-8"&gt;Remains same&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-8" name="mcq-options8" value="Decreases"&gt;
                            &lt;label for="mcq-option4-8"&gt;Decreases&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-9" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="W"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;The minimum drag is proportional to &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-9" name="mcq-options9" value="$W^2$"&gt;
                            &lt;label for="mcq-option1-9"&gt;$W^2$&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-9" name="mcq-options9" value="$W^{1/2}$"&gt;
                            &lt;label for="mcq-option2-9"&gt;$W^{1/2}$&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-9" name="mcq-options9" value="$W^{3/2}$"&gt;
                            &lt;label for="mcq-option3-9"&gt;$W^{3/2}$&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-9" name="mcq-options9" value="W"&gt;
                            &lt;label for="mcq-option4-9"&gt;W&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-10" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-subject="Basic Performance" data-type="NAT" data-explanation="" data-answer="-" data-max="16" data-min="14" data-precision="0"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;An aircraft has a steady rate of climb of 350m/s at sealevel and 175m/s at 2500m altitude. The time taken for this aircraft to climb from 500m to 3500m altitude is ----------. (neares integer answer)&lt;/p&gt;
                    &lt;input type="number" name="nat-options" id="nat-answer10" placeholder="Enter your answer here"&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-11" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-subject="Basic Performance" data-type="NAT" data-explanation="" data-answer="-" data-max="2" data-min="1" data-precision="1"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;The minimum drag speed is ------------ times of minimum power speed. (answer in one decimal)&lt;/p&gt;
                    &lt;input type="number" name="nat-options" id="nat-answer11" placeholder="Enter your answer here"&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-12" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Thrust required and power required increases"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;As Weight increases, &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-12" name="mcq-options12" value="Thrust required and power required decreases"&gt;
                            &lt;label for="mcq-option1-12"&gt;Thrust required and power required decreases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-12" name="mcq-options12" value="Thrust required and power required increases"&gt;
                            &lt;label for="mcq-option2-12"&gt;Thrust required and power required increases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-12" name="mcq-options12" value="Thrust required and power available increases"&gt;
                            &lt;label for="mcq-option3-12"&gt;Thrust required and power available increases&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option4-12" name="mcq-options12" value="Thrust required and power available increases"&gt;
                            &lt;label for="mcq-option4-12"&gt;Thrust required and power available increases&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div class="question" id="question-13" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="$(L/D)_{MAX}$"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;The maximum climb angle depends upon &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option1-13" name="mcq-options13" value="$(CL^{1/2}/ CD)_{MAX}$"&gt;
                            &lt;label for="mcq-option1-13"&gt;$(CL^{1/2}/ CD)_{MAX}$&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option2-13" name="mcq-options13" value="None of the above"&gt;
                            &lt;label for="mcq-option2-13"&gt;None of the above&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input type="radio" id="mcq-option3-13" name="mcq-options13" value="$(CL^{3/2}/ CD)_{MAX}$"&gt;
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                &lt;div class="question" id="question-14" data-correct-score="2" data-incorrect-score="-0.67" data-question-score="2" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="8.658km, 23.328m/s"&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
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                            Negative Marks: &lt;span style="color: red"&gt;-0.67&lt;/span&gt;
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                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;A glider having W=2000N, S=8.0 $m^2$, aspect ratio is 16, e=0.95, $C_{D_0}=0.015$ is launched from a height of 300m. Determine the maximum range and corresponding glide speed. &lt;/p&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
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                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;An aircraft has a level flight stalling speed of 60m/s EAS. As per V-n diagram, what is the minimum speed at which it should be designed to withstand the maximum vertical load factor of 9? &lt;/p&gt;
                    &lt;input type="number" name="nat-options" id="nat-answer15" placeholder="Enter your answer here"&gt;
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                &lt;div class="question" id="question-16" data-correct-score="2" data-incorrect-score="-0.67" data-question-score="2" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="(i) = b, (ii) = c, (iii) = a"&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
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                            Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                            Negative Marks: &lt;span style="color: red"&gt;-0.67&lt;/span&gt;
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                        &lt;div&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;A flying wing with a area of 27.75m2 has a NACA 2412 aerofoil section. The weight of the flying wing is 2270.663 Kg , Oswald lift deficiency factor is 0.95 and aspect ratio is 6. For a level flight at an altitude of 1500m, the relative density is 0.864 and the velocity is 160km/hr. Match the following (i)angle of attack(deg) a)11.29, (ii) induced drag coefficient(x10^-2) b)9.72, (iii)drag(x10^2 N) c)3.29. &lt;/p&gt;
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                &lt;div class="question" id="question-17" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Basic Performance" data-type="MCQ" data-explanation="" data-answer="Less than one"&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
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                    &lt;p&gt;For climbing flight the load factor is &lt;/p&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
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                    &lt;p&gt;A propeller aircraft weighs 50000N and a wing area of 30m2 . The reciprocating engine develops a power of 840 kW at sea level and a adjustable pitch propeller has a efficiency of 0.85. The drag polar of the aircraft is given by CD = 0.025+0.05CL2 and the maximum lift coefficient is 1.75. Determine the maximum and minimum speeds in level flight at sea level. &lt;/p&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
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                    &lt;p&gt;A glider weighing 5000N and an elliptical wing with a area of 10m2 is required to maintain a glide angle of 3 deg at a forward speed of 50m/s. Assuming CD0 = 0.015, find the aspect ratio of the glider. (answer in one decimal)&lt;/p&gt;
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                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
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                            Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
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                    &lt;p&gt;A turbojet airplane weighs 450000N and has a wing loading of 1450 N/m2. The drag polar of the aircraft is given by CD= 0.014+0.038CL^2and the maximum lift coefficient is 1.5 and the thrust T=20000 times of relative density. Determine the maximum and minimum speeds in level flight at sea level and at an altitude of 9000m where relative density is 0.3813. What is the absolute ceiling of this airplane? (answer in nearest integer)&lt;/p&gt;
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                    console.error("Fetch error:", error);
                    alert("There was an error processing your request.");
                    // Optionally show the user-info back if there was an error
                    document.getElementById('user-info').style.display = 'block';
                    document.getElementById('start-page').style.display = 'none';
                });
        });

        document.getElementById('calc-btn').addEventListener('click', function() {
            const calcContainer = document.getElementById('calc-container');

            const isVisible = calcContainer.style.display === 'block';

            if (isVisible) {
                calcContainer.style.display = 'none';
            } else {
                calcContainer.style.display = 'block';
                calcContainer.scrollIntoView({ behavior: 'smooth', block: 'center' });
            }
            const fullscreenContainer = document.getElementById('fullscreen-container');
            fullscreenContainer.appendChild(calcContainer);
        });

        const calcContainer = document.getElementById('calc-container');
        let offsetX, offsetY, isDragging = false;

        calcContainer.addEventListener('mousedown', (e) =&gt; {
            isDragging = true;
            offsetX = e.clientX - calcContainer.getBoundingClientRect().left;
            offsetY = e.clientY - calcContainer.getBoundingClientRect().top;
            document.addEventListener('mousemove', moveAt);
        });

        document.addEventListener('fullscreenchange', function() {
            const isFullscreenExited = !document.fullscreenElement &amp;&amp;
                !document.mozFullScreenElement &amp;&amp;
                !document.webkitFullscreenElement &amp;&amp;
                !document.msFullscreenElement;

            if (isFullscreenExited) {
                if (isAwaitingConfirmation &amp;&amp; !hasConfirmedSubmit) {
                    // User clicked submit but hasn't confirmed yet → DO NOT auto-submit
                    console.log("Fullscreen exited during confirmation. Not auto-submitting.");
                    return;
                }

                if (!hasConfirmedSubmit) {
                    // User exited fullscreen directly (via ESC or minimize) → Auto-submit
                    console.log("Fullscreen exited unexpectedly. Auto-submitting quiz.");
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';

                    const modal = document.getElementById('modal');
                    if (modal) {
                        modal.style.display = 'none';
                    }

                    document.getElementById('result-container').style.display = 'block';
                    displayResults();
                }
            }
        });


        document.addEventListener('mouseup', () =&gt; {
            if (isDragging) {
                isDragging = false;
                document.removeEventListener('mousemove', moveAt);
            }
        });

        function moveAt(e) {
            if (isDragging) {
                const newLeft = e.clientX - offsetX;
                const newTop = e.clientY - offsetY;
                calcContainer.style.left = newLeft + 'px';
                calcContainer.style.top = newTop + 'px';
            }
        }

        function initializeSubjectData() {
            const questionElements = document.querySelectorAll('.question');
            questionElements.forEach((question) =&gt; {
                const subject = question.getAttribute('data-subject');
                if (!subjectData[subject]) {
                    subjectData[subject] = {
                        markedForReview: new Set(),
                        answeredQuestions: new Set(),
                        correct: 0,
                        wrong: 0,
                        unattempted: 0,
                        score: 0,
                        totalQuestions: 0
                    };
                }
                timeTakenArray[subject] = [];
                subjectData[subject].totalQuestions++;
            });
        }

        document.getElementById('start-button').onclick = function() {
            document.getElementById('start-page').style.display = 'none';
            document.getElementById('fullscreen-container').style.display = 'block';
            startQuiz();
        };

        function startQuiz() {
            initializeSubjectData();
            // Automatically get the first subject from the questions
            const firstQuestion = document.querySelector('.question');
            if (firstQuestion) {
                const firstSubject = firstQuestion.getAttribute('data-subject');
                showSubject(firstSubject);
            }
            questionStartTimes[currentQuestionIndex] = Date.now();
            startCountdown();
            const fullscreenContainer = document.getElementById('fullscreen-container');
            fullscreenContainer.requestFullscreen();
            document.addEventListener('keydown', function(event) {
                event.preventDefault();
            });
            document.addEventListener('contextmenu', function(e) {
                e.preventDefault();
            });
            if (window.matchMedia("(orientation: portrait)").matches) {
                screen.orientation.lock("landscape").catch(function(error) {
                    console.error("Orientation lock failed: ", error);
                });
            }
        }

        // Utility: Shuffle an array using Fisher-Yates
        function shuffleArray(array) {
            for (let i = array.length - 1; i &gt; 0; i--) {
                const j = Math.floor(Math.random() * (i + 1));
                [array[i], array[j]] = [array[j], array[i]];
            }
            return array;
        }

        function showSubject(subject) {
            // recordTimeTaken();
            currentSubject = subject;

            // Get and shuffle questions for the selected subject
            const allQuestions = Array.from(document.querySelectorAll(`.question[data-subject="${subject}"]`));
            questions = shuffleArray(allQuestions);

            // Hide all questions first
            document.querySelectorAll('.question').forEach((q) =&gt; q.style.display = 'none');

            currentQuestionIndex = 0;
            updateQuestionDisplay();
            updateFooterButtons();
            updateQuestionPalette();
            questionStartTimes[currentQuestionIndex] = Date.now();

        }

        function updateQuestionDisplay() {
            // Hide all questions
            document.querySelectorAll('.question').forEach((question) =&gt; {
                question.style.display = 'none';
            });

            if (questions.length &gt; 0) {
                const currentQuestion = questions[currentQuestionIndex];
                currentQuestion.style.display = 'block';

                // Show or hide numeric keypad based on type
                if (currentQuestion.getAttribute('data-type') === 'NAT') {
                    document.getElementById('numeric-keypad').style.display = 'block';
                } else {
                    document.getElementById('numeric-keypad').style.display = 'none';
                }

                // // Store original content once to allow re-shuffling only visible options
                const originalContent = currentQuestion.getAttribute('data-original-content');
                if (!originalContent) {
                    currentQuestion.setAttribute('data-original-content', currentQuestion.innerHTML);
                }

                const baseContent = currentQuestion.getAttribute('data-original-content');
                const indexText = `&lt;div style="font-weight:bold; margin-bottom:5px; font-size:14px;"&gt;Question ${currentQuestionIndex + 1}&lt;/div&gt;`;
                currentQuestion.innerHTML = indexText + baseContent;

                // Shuffle only the visible order of options (not values or labels)
                const optionsContainer = currentQuestion.querySelector('.options');
                if (optionsContainer) {
                    const optionDivs = Array.from(optionsContainer.children);

                    // Shuffle visual order
                    for (let i = optionDivs.length - 1; i &gt; 0; i--) {
                        const j = Math.floor(Math.random() * (i + 1));
                        [optionDivs[i], optionDivs[j]] = [optionDivs[j], optionDivs[i]];
                    }

                    // Re-append shuffled elements
                    optionDivs.forEach(div =&gt; optionsContainer.appendChild(div));
                }
            }
        }

        function updateFooterButtons() {
            document.getElementById('prev').style.display = currentQuestionIndex === 0 ? 'none' : 'inline';
            document.getElementById('next').style.display = currentQuestionIndex === questions.length - 1 ? 'none' : 'inline';
            document.getElementById('footer_buttons').style.display = questions.length &gt; 0 ? 'block' : 'none';
        }

        document.getElementById('prev').onclick = function() {
            if (currentQuestionIndex &gt; 0) {
                recordTimeTaken();
                handleQuestionStateBeforeChange();
                currentQuestionIndex--;
                updateQuestionDisplay();
                updateFooterButtons();
                updateQuestionPalette();
                questionStartTimes[currentQuestionIndex] = Date.now();
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            }
        }

        document.getElementById('next').onclick = function() {
            if (currentQuestionIndex &lt; questions.length - 1) {
                recordTimeTaken();
                handleQuestionStateBeforeChange();
                currentQuestionIndex++;
                updateQuestionDisplay();
                updateFooterButtons();
                updateQuestionPalette();
                questionStartTimes[currentQuestionIndex] = Date.now();
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            }
        }

        document.getElementById('clear').onclick = function() {
            const currentQuestion = questions[currentQuestionIndex];
            currentQuestion.querySelectorAll('input:checked').forEach(input =&gt; input.checked = false);
            subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
            const fullscreenContainer = document.getElementById('fullscreen-container');
            fullscreenContainer.requestFullscreen();
            if (window.matchMedia("(orientation: portrait)").matches) {
                screen.orientation.lock("landscape").catch(function(error) {
                    console.error("Orientation lock failed: ", error);
                });
            }

            updateQuestionPalette();
        }

        function recordTimeTaken() {
            const questionEndTime = Date.now();
            const questionStartTime = questionStartTimes[currentQuestionIndex];
            const timeTaken = (questionEndTime - questionStartTime) / 1000;
            const subject = currentSubject;
            if (!timeTakenArray[subject]) {
                timeTakenArray[subject] = {};
            }
            if (!timeTakenArray[subject][currentQuestionIndex]) {
                timeTakenArray[subject][currentQuestionIndex] = 0;
            }
            timeTakenArray[subject][currentQuestionIndex] += timeTaken;
            questionStartTimes[currentQuestionIndex] = questionEndTime;
        }

        document.getElementById('submit').onclick = function() {
            console.log("Submit button clicked!");
            recordTimeTaken();

            isAwaitingConfirmation = true; // User clicked submit, waiting for confirm

            const modal = document.getElementById('myModal');
            modal.style.display = 'block';

            // Exit fullscreen early
            const exitFullScreen =
                document.exitFullscreen ||
                document.mozCancelFullScreen ||
                document.webkitExitFullscreen ||
                document.msExitFullscreen;

            if (exitFullScreen) {
                exitFullScreen.call(document);
                console.log("Exited fullscreen.");
            }

            document.getElementById('confirmSubmit').onclick = function() {
                console.log("Confirm submit clicked!");
                hasConfirmedSubmit = true;
                isAwaitingConfirmation = false; // No longer awaiting

                // Hide quiz elements
                document.getElementById('fullscreen-container').style.display = 'none';
                document.getElementById('question-palette').style.display = 'none';
                modal.style.display = 'none';
                document.getElementById('result-container').style.display = 'block';
                displayResults();

                // Show Ad Modal
                const adModal = document.getElementById('adModal');
                const adCloseButton = document.getElementById('adClose');

                if (adModal) {
                    adModal.style.display = 'none';

                    setTimeout(() =&gt; {
                        if (adCloseButton) {
                            adCloseButton.style.display = 'inline';
                        }
                    }, 5000);

                    if (adCloseButton) {
                        adCloseButton.onclick = function() {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block';
                            displayResults();
                        };
                    }

                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block';
                            showResult();
                        }
                    }, 10000);
                }

                clearInterval(timerInterval);
            };

            document.getElementById('cancelSubmit').onclick = function() {
                console.log("Cancel submit clicked! Closing modal.");
                modal.style.display = 'none';

                isAwaitingConfirmation = false; // Cancel confirmation

                const fullscreenContainer = document.getElementById('fullscreen-container');
                if (fullscreenContainer.requestFullscreen) {
                    fullscreenContainer.requestFullscreen();
                }

                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            };
        };

        function displayResults() {
            document.getElementById('result-container').style.display = 'block';
            document.getElementById('user-name-display').innerText = userName;
            showResult();
            // window.location.href = './results.html'; 
        }

        document.getElementById('mark-for-review').onclick = function() {
            const subjectMarks = subjectData[currentSubject].markedForReview;
            const currentQuestion = questions[currentQuestionIndex];
            const userAnswer = getUserAnswer(currentQuestion);
            const fullscreenContainer = document.getElementById('fullscreen-container');
            fullscreenContainer.requestFullscreen();
            if (window.matchMedia("(orientation: portrait)").matches) {
                screen.orientation.lock("landscape").catch(function(error) {
                    console.error("Orientation lock failed: ", error);
                });
            }

            if (subjectMarks.has(currentQuestionIndex)) {
                subjectMarks.delete(currentQuestionIndex);
            } else {
                subjectMarks.add(currentQuestionIndex);
            }
            if (userAnswer) {
                subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
            } else {
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
            }
            updateQuestionPalette();
        }

        function handleQuestionStateBeforeChange() {
            const currentQuestion = questions[currentQuestionIndex];
            const userAnswer = getUserAnswer(currentQuestion);

            // Save the user's answer
            if (userAnswer) {
                subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
            } else {
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
            }

            // Always mark the question as seen
            markAsSeen(currentQuestionIndex);
        }

        function updateQuestionStats() {
            // Count answered questions (green buttons)
            const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'green').length;

            // Count answered and marked for review questions (purple buttons with purple-dot class)
            const answeredMarkedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.classList.contains('purple-dot') &amp;&amp; button.style.backgroundColor === 'purple').length;

            // Count marked for review questions (just purple buttons without the purple-dot class)
            const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'purple' &amp;&amp; !button.classList.contains('purple-dot')).length;

            // Total questions in the current subject
            const totalQuestions = questions.length;

            // Count unanswered questions (red buttons)
            const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'red').length;

            // Count not visited questions (black buttons)
            const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'black').length;

            // Update the counts in the HTML
            document.getElementById('answered-count').textContent = `${answeredCount}`;
            document.getElementById('unanswered-count').textContent = `${unansweredCount}`;
            document.getElementById('review-count').textContent = `${markedForReviewCount}`;
            document.getElementById('answered-review-count').textContent = `${answeredMarkedForReviewCount}`;
            document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
        }

        function updateQuestionPalette() {
            const palette = document.getElementById('question-palette');
            palette.innerHTML = '';
            const subjectHeading = document.createElement('h3');
            subjectHeading.textContent = `${currentSubject} Questions`;
            palette.appendChild(subjectHeading);

            questions.forEach((question, index) =&gt; {
                const button = document.createElement('button');
                button.textContent = index + 1;
                button.classList.toggle('active', index === currentQuestionIndex);

                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }

                const subjectMarks = subjectData[currentSubject].markedForReview;
                const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                // Set button background color based on question state
                if (subjectMarks.has(index) &amp;&amp; subjectAnswered.has(index)) {
                    button.classList.add('purple-dot');
                    button.style.backgroundColor = 'purple'; // Answered and Marked for Review
                } else if (subjectAnswered.has(index)) {
                    button.style.backgroundColor = 'green'; // Answered
                } else if (subjectMarks.has(index)) {
                    button.style.backgroundColor = 'purple'; // Marked for Review
                } else if (questions[index].seen) {
                    button.style.backgroundColor = 'red'; // Unanswered
                } else {
                    button.style.backgroundColor = 'black'; // Not Visited
                }

                // Add event handler for question button
                button.onclick = () =&gt; {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex = index;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    updateQuestionStats(); // Update stats when changing questions
                };

                palette.appendChild(button);
            });

            updateQuestionStats(); // Update stats when rendering the palette
        }

        function markAsSeen(questionIndex) {
            questions[questionIndex].seen = true;
        }

        function startCountdown() {
            targetTime = Date.now() + countdownSeconds * 1000;
            updateTimerDisplay();

            timerInterval = setInterval(() =&gt; {
                if (Date.now() &gt;= targetTime) {
                    clearInterval(timerInterval);
                    document.getElementById('timer').textContent = "Time's Up!";

                    // DIRECTLY submit the quiz when time is up
                    recordTimeTaken();

                    // Hide quiz elements
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    document.getElementById('result-container').style.display = 'block';

                    // Display results immediately
                    displayResults();

                    // Exit fullscreen if needed
                    const exitFullScreen =
                        document.exitFullscreen ||
                        document.mozCancelFullScreen ||
                        document.webkitExitFullscreen ||
                        document.msExitFullscreen;

                    if (exitFullScreen) {
                        exitFullScreen.call(document);
                    }
                } else {
                    updateTimerDisplay();
                }
            }, 1000);
        }

        function updateTimerDisplay() {
            const remainingTime = targetTime - Date.now();
            const minutes = Math.floor(remainingTime / 60000);
            const seconds = Math.floor((remainingTime % 60000) / 1000);
            document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
            if (remainingTime &lt; 600000) {
                document.getElementById('timer').style.color = 'red';
            } else {
                document.getElementById('timer').style.color = '';
            }
        }

        function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
            const userAnswerNum = parseFloat(userAnswer);
            const userDecimals = (userAnswer.split('.')[1] || '').length;
            const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;

            // Check if the answer has the correct number of decimal places
            const isCorrectPrecision = userDecimals === precision;

            return isInRange &amp;&amp; isCorrectPrecision;
        }

        function getUserAnswer(question) {
            const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
            const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
            const textInput = Array.from(question.querySelectorAll('input[type="number"]')).map(input =&gt; input.value.trim());
            return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
        }

        function addToInput(value) {
            // Get the current question's input field
            const inputField = questions[currentQuestionIndex].querySelector('input[type="number"]');
            if (inputField) {
                inputField.value += value; // Append the value to the current input field
            }
        }

        function clearInput() {
            // Get the current question's input field
            const inputField = questions[currentQuestionIndex].querySelector('input[type="number"]');
            if (inputField) {
                inputField.value = ''; // Clear the current input field
            }
        }

        function toggleSign() {
            // Get the current question's input field
            const inputField = questions[currentQuestionIndex].querySelector('input[type="number"]');
            if (inputField) {
                if (inputField.value.startsWith('-')) {
                    inputField.value = inputField.value.substring(1); // Remove the negative sign
                } else {
                    inputField.value = '-' + inputField.value; // Add the negative sign
                }
            }
        }

        document.getElementById('restart').addEventListener('click', function() {
            // Reset quiz state
            currentQuestionIndex = 0;
            subjectData = {};
            timeTakenArray = {};

            // Show quiz
            document.getElementById('question-palette').style.display = 'block';

            // Call the function to start the quiz
            startQuiz();
        });

        function showResult() {
            const subjects = {};
            const questions = document.querySelectorAll('.question');

            const userName = document.getElementById('user-name')?.value || 'Anonymous';
            const userNameDisplay = document.getElementById('user-display');
            if (userNameDisplay) userNameDisplay.textContent = userName;


            questions.forEach((question, i) =&gt; {
                const subject = question.getAttribute('data-subject');
                if (!subjects[subject]) {
                    subjects[subject] = {
                        correct: 0,
                        wrong: 0,
                        unattempted: 0,
                        score: 0,
                        totalCorrectScore: 0,
                        timeSpent: [],
                        time: 0,
                        questions: [],
                    };
                }

                const questionType = question.getAttribute('data-type');
                const correctAnswer = question.getAttribute('data-answer')?.split(';').sort().join(';');
                const userAnswer = getUserAnswer(question);
                const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                const questionPara = question.querySelector('p')?.outerHTML || '';
                const questionImage = question.querySelector('img')?.outerHTML || '';
                const questionText = questionPara + questionImage;

                const optionElements = question.querySelectorAll('.options div label');
                const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());

                const questionDetail = {
                    questionText,
                    userAnswer: userAnswer || 'Not answered',
                    correctAnswer,
                    result: 'Wrong',
                    type: questionType,
                    correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                    incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                    options,
                    question,
                    explanation
                };

                evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);
                subjects[subject].questions.push(questionDetail);

                const timeForThisQuestion = timeTakenArray[subject]?.[i] || 0;
                subjects[subject].timeSpent.push(timeForThisQuestion);
                subjects[subject].time += timeTakenArray[subject]?.[i] || 0;
                subjects[subject].totalCorrectScore += questionDetail.correctScore;
            });


            displayDetailedResults(subjects);
            displayDetailed(subjects);
            renderTimeSpentChart(subjects);
            checkUserPerformance(subjects);
            sendResultsToSheet(subjects, userName);
        }

        function displayDetailedResults(subjects) {
            const resultBody = document.getElementById('result-body');
            resultBody.innerHTML = '';

            let totalmarks = 0;
            let totalScore = 0;
            let totalCorrect = 0;
            let totalWrong = 0;
            let totalUnattempted = 0;
            let totalTimeSpent = 0;


            for (const subject in subjects) {
                const subjectResult = subjects[subject];
                let subjectTimeSpent = 0;

                totalScore += subjectResult.score;
                totalCorrect += subjectResult.correct;
                totalWrong += subjectResult.wrong;
                totalUnattempted += subjectResult.unattempted;
                totalmarks += subjectResult.totalCorrectScore;



                subjectResult.questions.forEach((_, index) =&gt; {
                    const timeSpent = timeTakenArray[subject]?.[index] || 0;
                    subjectTimeSpent += timeSpent;
                });

                totalTimeSpent += subjectTimeSpent;

                const subjectMinutes = Math.floor(subjectTimeSpent / 60);
                const subjectSeconds = Math.floor(subjectTimeSpent % 60).toString().padStart(2, '0');

                resultBody.innerHTML += `
                    &lt;tr class="category-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                        &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${subjectMinutes.toString().padStart(2, '0')} min:${subjectSeconds} sec&lt;/td&gt;
                        &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                        &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                        &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                    &lt;/tr&gt;`;
            }

            const totalMinutes = Math.floor(totalTimeSpent / 60);
            const totalSeconds = Math.floor(totalTimeSpent % 60).toString().padStart(2, '0');

            resultBody.innerHTML += `
                &lt;tr class="total-row"&gt;
                    &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                    &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                    &lt;td&gt;${totalMinutes.toString().padStart(2, '0')} min:${totalSeconds} sec&lt;/td&gt;
                    &lt;td&gt;${totalCorrect}&lt;/td&gt;
                    &lt;td&gt;${totalWrong}&lt;/td&gt;
                    &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                &lt;/tr&gt;`;
            // Prepare total row data
            const totalData = {
                user: user,
                subject: titlequiz,
                score: totalScore.toFixed(2),
                time: `${totalMinutes.toString().padStart(2, '0')} min : ${totalSeconds.toString().padStart(2, '0')} sec`,
                correct: totalCorrect,
                wrong: totalWrong,
                unattempted: totalUnattempted,
                totalMarks: totalmarks.toFixed(2)
            };

            // Send data to Google Apps Script
            fetch('https://script.google.com/macros/s/AKfycbwIKNfe9P7dSIbmLLQM6K-A1g64GkQ3klnr1eEcTkylMXVjfVn7-DT2V9VeWlHiFRvK-Q/exec', {
                method: 'POST',
                mode: 'no-cors', // Use 'cors' if handling response
                headers: {
                    'Content-Type': 'application/json'
                },
                body: JSON.stringify(totalData)
            });

        }

        function checkUserPerformance(subjects) {
            let totalScore = 0;
            let totalMarks = 0;
            for (const subject in subjects) {
                totalScore += subjects[subject].score;
                totalMarks += subjects[subject].totalCorrectScore;
            }
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                        &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;

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&lt;/html&gt;</description><link>https://aerogatetopper.blogspot.com/2025/05/basic-performance.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-3898158933458123371</guid><pubDate>Mon, 20 Jan 2025 14:18:00 +0000</pubDate><atom:updated>2025-03-23T11:18:45.322+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">INTERVIEW</category><title>DRDO Interview Questions for Aerospace Engineering Part- 2</title><description>
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&lt;body&gt;
  &lt;p&gt;Welcome to an insightful exploration of core concepts in aerospace engineering and fluid mechanics. This post delves into a series of thought-provoking questions, offering clear, in-depth answers on topics ranging from rocket propulsion and drag forces to column buckling and Reynolds number effects. Whether you're a budding engineer, a seasoned professional, or simply fascinated by the science of flight and propulsion, this collection of Q&amp;A is designed to broaden your understanding.

To make your learning experience even more interactive, we've integrated a feature that allows you to easily toggle between questions and answers. Plus, you can conveniently download the answers in an Excel file for reference or further study. Just click the "Show Answer" button, and when you're ready, download the full set of answers with a simple click.

Dive in and unlock the knowledge behind the forces that shape the world of engineering and flight.&lt;/p&gt;

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&lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: Can you explain the concept of specific impulse in rocket propulsion and its significance in determining rocket performance?&lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: Specific impulse (often denoted as "Isp") is a fundamental concept in rocket propulsion that plays a important role in determining the performance and efficiency of a rocket engine. It's a measure of how effectively a rocket engine can convert the propellant's mass flow rate into thrust.&lt;/div&gt;
&lt;/div&gt;

&lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: What are the different propellant compositions commonly used in rocket engines, and how do they affect the overall performance of the rocket? &lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: Rocket engines use various propellant compositions to generate thrust. These propellants are typically a combination of fuels and oxidizers that undergo chemical reactions to produce the hot gases expelled at high speeds to create thrust. 
  1. Liquid Bipropellant
  2. Solid Propellant
  3. Hybrid Propellant
  4. Cryogenic Propellant
  Propellant composition affects several aspects of rocket performance:
  a. Specific Impulse
  b. Thrust
  c. Storability and Handling
  d. Toxicity and Environmental Impact&lt;/div&gt;
&lt;/div&gt;

  &lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: Can you explain the different types of drag encountered by a body moving through a fluid? How do they differ from each other? &lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: Drag is the force that opposes the motion of a body as it moves through a fluid (such as air or water). There are several types of drag encountered by a body in fluid motion, each resulting from different physical mechanisms. These types of drag are:
    1. Pressure Drag:It is occurs due to the pressure difference between the front and rear sides of an object moving through a fluid. 
    2. Skin-Friction Drag: It  is caused by the viscosity of the fluid. 
    3. Induced Drag: It is a byproduct of generating lift, such as in the case of an aircraft's wings. When an airfoil generates lift. It also creates a vortex at its wingtips. This vortex generates additional drag that opposes the aircraft's motion.
    4. Wave Drag:  It generates due shockwaves and pressure waves.
    5. Parasitic Drag: It is a combination of pressure drag, friction drag, and other non-lift-related drags.   &lt;/div&gt;
&lt;/div&gt;
  
  &lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: When measuring drag for flow across a sphere, what experimental techniques or methods are commonly employed? &lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: Measuring drag for flow across a sphere involves a range of experimental techniques and methods that aim to accurately quantify the forces and characteristics of the flow. Here are some commonly employed techniques:
    1. Force Balance (Wind Tunnel Testing)
    2. Pressure Tap Measurements
    3. Hot-Wire Anemometry
    4. Direct Numerical Simulation (DNS) 
    5. Computational Fluid Dynamics (CFD)
    6. Boundary Layer Measurements
    &lt;/div&gt;
&lt;/div&gt;
  
  &lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: How does the Reynolds number affect the drag coefficient for flow across a sphere? Explain the relationship between these two parameters.&lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: The Reynolds number has a substantial impact on the drag coefficient for flow across a sphere. At low Reynolds numbers, the drag coefficient is relatively constant and low due to laminar flow behavior. As the Reynolds number increases and the flow becomes more turbulent, the drag coefficient increases significantly due to the formation of larger wake regions and increased pressure drag. The specific relationship between Reynolds number and drag coefficient varies depending on the flow regime and the sphere's characteristics, but understanding this relationship is crucial for predicting and optimizing the behavior of objects moving through a fluid.&lt;/div&gt;
&lt;/div&gt;
  
  &lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: Can you explain the concept of critical buckling load in the context of column buckling experiments?&lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A:  In the context of column buckling experiments, the critical buckling load is a fundamental concept that describes the point at which a slender column under axial compression becomes unstable and starts to buckle or deform laterally. This is a crucial consideration in structural engineering, especially when designing columns or members that support axial loads, like the columns in buildings, bridges, or other structures.
    The critical buckling load is the maximum axial load that a column can withstand without buckling occurring. It's the point at which the column transitions from a stable state to an unstable state. &lt;/div&gt;
&lt;/div&gt;
  
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  &lt;div class="question"&gt;Q: What are some common methods used to measure and analyze the buckling behavior of columns?&lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: Measuring and analyzing the buckling behavior of columns is a critical aspect of structural engineering and materials science. Understanding how columns behave under axial compression is essential for designing safe and efficient structures. Here are some common methods used to measure and analyze the buckling behavior of columns:
    1. Experimental Testing
    2. Buckling Test
    3. Finite Element Analysis (FEA)
    4. Analytical Solution
    5. Numerical Simulation
    6. Theoritical Models&lt;/div&gt;
&lt;/div&gt;
  
  &lt;div class="qa-container"&gt;
  &lt;div class="question"&gt;Q: In steady level flight, which direction does the thrust of an aircraft act in relation to its motion?&lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: In steady level flight, the thrust of an aircraft acts forward in the same direction as its motion.
    In steady level flight, four main forces are:
    1. Thrust
    2. Drag
    3. Lift
    4. Weight&lt;/div&gt;
&lt;/div&gt;
  
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  &lt;div class="question"&gt;Q: How does the angle of attack affect lift and drag during steady level flight? &lt;/div&gt;
  &lt;button class="toggle-button"&gt;Show Answer&lt;/button&gt;
  &lt;div class="answer"&gt;A: during steady level flight, the angle of attack has a direct impact on lift and drag:

Increasing the angle of attack initially increases lift due to increased pressure difference.
Beyond a certain point (critical angle of attack), the airflow separation reduces lift and can decrease drag.
Beyond the critical angle of attack, lift continues to decrease while drag increases significantly due to flow separation effects.&lt;/div&gt;
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</description><link>https://aerogatetopper.blogspot.com/2025/01/drdo-interview-questions-for-aerospace.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-3349241808298333666</guid><pubDate>Mon, 28 Oct 2024 17:24:00 +0000</pubDate><atom:updated>2025-05-01T13:56:56.113+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Linear Algebra - 4 </title><description>&lt;html lang="en"&gt;

&lt;head&gt;
    &lt;title&gt;Linear Algebra Topic-wise Online Quiz&lt;/title&gt;
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    &lt;div id="start-page" style="display: none;"&gt;
        &lt;center&gt;
            &lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;
        &lt;/center&gt;
        &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
        &lt;p&gt;&lt;/p&gt;
        &lt;ol style="text-align: left;"&gt;
            &lt;li&gt;The total duration of the examination is 45 minutes .&lt;/li&gt;
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            &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
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                &lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;
                &lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;
                &lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;
                &lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;
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            &lt;li&gt;
                You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;
        &lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
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                &lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;
                &lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;
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                Procedure for answering a numerical answer type question:&lt;/li&gt;
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                &lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;
                &lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;
                &lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;
                &lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;
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                To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;
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                            &lt;p&gt;Linear Algebra&lt;/p&gt;
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                        &lt;b&gt;
                            &lt;h1&gt;AERO GATE TOPPER&lt;/h1&gt;
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                    &lt;!-- Question 1 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The rank of a matrix product is determined by the smallest rank of the matrices being multiplied. Since B is invertible, it does not affect the rank of A."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;1. If matrix A has a rank of 2, what is the rank of the matrix formed by multiplying A with a 2x2 invertible matrix B?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options1" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options1" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;2&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options1" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;4&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options1" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Cannot be determined&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 2 --&gt;
                    &lt;div class="question" data-answer="2" data-correct-score="2" data-incorrect-score="0" data-max="2" data-min="2" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="To determine the rank, examine the matrix rows for linear dependence. The rank here is based on the number of independent rows."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;2. Given the matrix A \[ A = \begin{pmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \\ 7 &amp; 8 &amp; 9 \end{pmatrix} \] find the rank of A.&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer2" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 3 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The determinant of a matrix is the product of its eigenvalues. Here, multiply 2, -3, and 5 to find the determinant."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;3. For a matrix A with eigenvalues 2, -3, and 5, what is the determinant of A?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options3" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;10&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options3" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;0&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options3" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;-30&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options3" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;None of these&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 4 --&gt;
                    &lt;div class="question" data-answer="1" data-correct-score="2" data-incorrect-score="0" data-max="1" data-min="1" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="If A satisfies A² - A = 0, it is idempotent, which limits the possible distinct eigenvalues."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;4. If a matrix A satisfies A² - A = 0, where A is a 2x2 matrix, how many distinct eigenvalues does A have?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer4" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 5 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="An invertible matrix has a non-zero determinant by definition, which also implies none of its eigenvalues is zero."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;5. Which of the following statements is true for an invertible matrix A?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;A has at least one eigenvalue equal to zero&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;A is singular&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;A is symmetric&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The determinant of A is non-zero&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 6 --&gt;
                    &lt;!-- Question 6 --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="An orthogonal matrix with a determinant of -1 must have at least one eigenvalue equal to -1, as the product of the eigenvalues equals the determinant."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;6. Let \( A \) be a 3x3 orthogonal matrix with a determinant of -1. Which of the following is true about the eigenvalues of \( A \)?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options6" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;At least one eigenvalue is -1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options6" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;All eigenvalues are real and positive&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options6" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;All eigenvalues have a magnitude of 1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options6" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;No eigenvalues are real&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;


                    &lt;!-- Question 7 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The rank of a matrix is defined as the maximum number of linearly independent column vectors in the matrix. It can also be determined by reducing the matrix to row echelon form."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;7. What is the rank of the following matrix? \[ C = \begin{pmatrix} 1 &amp; 2 &amp; 3 \\ 0 &amp; 0 &amp; 0 \\ 4 &amp; 5 &amp; 6 \end{pmatrix} \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options7" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options7" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;2&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options7" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;3&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options7" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;0&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 8 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The characteristic polynomial of a matrix is obtained by calculating the determinant of (A - λI), where λ is an eigenvalue and I is the identity matrix. The roots of this polynomial are the eigenvalues."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;8. What is the characteristic polynomial of the matrix D = \begin{pmatrix} 2 &amp; 1 \\ 1 &amp; 2 \end{pmatrix} ?
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;\( \lambda^2 - 3\lambda + 1 \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;\( \lambda^2 - 4\lambda + 3 \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;\( \lambda^2 + 1 \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;\( \lambda^2 - 1 \)&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 9 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="MCQ" data-explanation="Orthogonal vectors \( u \) and \( v \) have an inner product (dot product) equal to 0, which defines their orthogonality in an inner product space."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;9. Which of the following is true for any two orthogonal vectors \( u \) and \( v \) in an inner product space?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options9" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;u · v = 1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options9" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;u · v = 0&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options9" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;u + v = 0&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options9" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;None of these&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;


                    &lt;!-- Question 10 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="A linear transformation is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. A function that does not satisfy this property is not a linear transformation."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;10. Which of the following is NOT a property of a linear transformation?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options10" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;It preserves vector addition&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options10" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;It preserves scalar multiplication&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options10" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;It maps zero vector to zero vector&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options10" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It can map vectors to scalars&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 11 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The null space of a matrix is the set of all vectors \( v \) such that \( Av = 0 \). The dimension of the null space is related to the rank-nullity theorem."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;11. Which of the following statements about the null space of a matrix A is TRUE?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options11" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;It consists of all columns of A&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options11" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;It contains the zero vector and can include non-zero vectors&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options11" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;It is equal to the column space of A&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options11" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It is the same as the range of A&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 12 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The inverse of a matrix exists if the matrix is square and has a non-zero determinant. If the determinant is zero, the matrix is singular and does not have an inverse."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;12. Which of the following matrices does NOT have an inverse?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options12" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;\( \begin{pmatrix} 1 &amp; 0 \\ 0 &amp; 1 \end{pmatrix} \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options12" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;\( \begin{pmatrix} 1 &amp; 2 \\ 3 &amp; 4 \end{pmatrix} \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options12" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;\( \begin{pmatrix} 1 &amp; 2 \\ 2 &amp; 4 \end{pmatrix} \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options12" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;\( \begin{pmatrix} 0 &amp; 1 \\ 1 &amp; 0 \end{pmatrix} \)&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 13 --&gt;
                    &lt;div class="question" data-answer="0" data-correct-score="2" data-incorrect-score="0" data-max="0" data-min="0" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="To calculate the determinant of a 3x3 matrix, use the rule of Sarrus or the cofactor expansion."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;13. Calculate the determinant of the matrix \[ F = \begin{pmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \\ 7 &amp; 8 &amp; 9 \end{pmatrix} \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer13" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 14 --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The eigenvalues of a triangular matrix are simply the diagonal elements. For a diagonal matrix, the eigenvalues are the elements on the diagonal."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;14. What are the eigenvalues of the matrix G = \begin{pmatrix} 4 &amp; 0 \\ 0 &amp; 5 \end{pmatrix} ?
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options14" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;4 and 5&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options14" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;0&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options14" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;4, 5, and 0&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options14" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;None of the above&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 15 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Gram-Schmidt process is used to orthogonalize a set of vectors in an inner product space, ensuring that the resulting set of vectors is orthogonal and spans the same space."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;15. What is the purpose of the Gram-Schmidt process?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;To find eigenvalues of a matrix&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options15" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;To orthogonalize a set of vectors&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;To solve systems of equations&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;To compute the determinant of a matrix&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 16 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The characteristic polynomial of a matrix A is given by \( p(\lambda) = \det(A - \lambda I) \), where I is the identity matrix. The roots of this polynomial are the eigenvalues of A."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;16. How do you calculate the characteristic polynomial of a matrix A?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options16" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;By finding the trace of A&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options16" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;By computing \( \det(A - \lambda I) \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options16" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;By calculating the inverse of A&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options16" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;By diagonalizing A&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 17 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation, which means that if p(λ) is the characteristic polynomial of A, then p(A) = 0."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;17. What does the Cayley-Hamilton theorem state?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options17" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;A matrix can be inverted if it is square&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options17" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Eigenvalues can be computed from the determinant&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options17" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Every square matrix satisfies its own characteristic equation&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options17" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The rank of a matrix equals the number of its eigenvalues&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 18 --&gt;
                    &lt;div class="question" data-answer="2" data-correct-score="2" data-incorrect-score="0" data-max="2" data-min="2" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="The singular value decomposition (SVD) of a matrix A can be expressed as \( A = U \Sigma V^T \), where U and V are orthogonal matrices and \( \Sigma \) is a diagonal matrix containing the singular values of A. The number of non-zero singular values equals the rank of the matrix."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;18. Find the number of non-zero singular values for the matrix \[ H = \begin{pmatrix} 1 &amp; 2 \\ 0 &amp; 0 \\ 3 &amp; 4 \end{pmatrix} \].&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer18" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;


                    &lt;!-- Question 19 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Jordan normal form of a matrix is a block diagonal matrix where each block is a Jordan block corresponding to an eigenvalue, capturing both the eigenvalue and its algebraic and geometric multiplicities."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;19. What is the Jordan normal form of a matrix used for?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options19" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;To diagonalize the matrix&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options19" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;To compute the determinant&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options19" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;To find eigenvectors&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options19" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;To represent the structure of a matrix in terms of its eigenvalues&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 20 --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The RREF of a matrix is unique and can be achieved through a series of elementary row operations, providing insights into the solution space of a linear system."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;20. What does RREF stand for in the context of linear systems?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options20" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Reduced Row Echelon Form&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options20" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Regular Row Element Format&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options20" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Reduced Rank Element Framework&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options20" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Randomized Row Entry Format&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 21 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="A vector space is a set of vectors where addition and scalar multiplication are defined and satisfy certain properties (closure, associativity, commutativity, identity element, and invertibility)."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;21. Which of the following correctly defines a vector space?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options21" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;A set of vectors with only scalar multiplication&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options21" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;A collection of matrices with no defined operations&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options21" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;A set of vectors closed under addition and scalar multiplication&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options21" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;A set of numbers that can be added&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 22 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Gram-Schmidt process is used to orthogonalize a set of vectors in an inner product space, producing an orthonormal basis from a linearly independent set of vectors."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;22. What is the purpose of the Gram-Schmidt process?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options22" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;To find the determinant of a matrix&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options22" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;To orthogonalize a set of vectors&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options22" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;To compute the rank of a matrix&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options22" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;To solve a system of linear equations&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 23 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="A nilpotent matrix is defined as a square matrix N for which \( N^k = 0 \) for some positive integer k."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;23. What characterizes a nilpotent matrix?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options23" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;It has non-zero eigenvalues&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options23" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;It can be diagonalized&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options23" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;It has an inverse&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options23" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It satisfies \( N^k = 0 \) for some integer k&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 24 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="An orthogonal matrix is defined by the property that its transpose equals its inverse: \( A^T A = I \), where I is the identity matrix."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;24. Which property defines an orthogonal matrix?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options24" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The matrix is square&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options24" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The determinant is 1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options24" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The transpose equals the inverse&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options24" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The trace is zero&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;


                    &lt;!-- Question 25 --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The spectral theorem states that any symmetric matrix can be diagonalized by an orthogonal matrix, meaning it can be expressed in the form \( A = QDQ^T \), where Q is orthogonal and D is diagonal."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;25. What does the spectral theorem state for symmetric matrices?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options25" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;They can be diagonalized by an orthogonal matrix&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options25" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;They are always invertible&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options25" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;They have complex eigenvalues&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options25" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;They cannot be represented in RREF&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;


                    &lt;!-- Question 26 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The rank-nullity theorem states that for a linear transformation from a finite-dimensional vector space, the rank (dimension of the image) plus the nullity (dimension of the kernel) equals the dimension of the domain."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;26. What does the rank-nullity theorem state?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options26" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The rank is always greater than the nullity&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options26" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Rank + Nullity = Dimension of Domain&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options26" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Rank = Nullity&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options26" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The null space is always one-dimensional&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 27 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="An eigenvalue of a square matrix A is defined by the equation \( Av = \lambda v \), where \( \lambda \) is the eigenvalue and v is the corresponding eigenvector."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;27. How is an eigenvalue defined for a matrix A?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options27" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;It is the sum of the diagonal elements&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options27" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;It is the determinant of the matrix&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options27" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;It is defined by \( Av = \lambda v \)&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options27" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It is the product of the eigenvectors&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 28 --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="A matrix is diagonalizable if it has enough linearly independent eigenvectors to form a basis for the vector space, allowing it to be expressed in the form \( PDP^{-1} \)."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;28. When is a matrix considered diagonalizable?&lt;/p&gt;
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                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options28" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;If it has enough linearly independent eigenvectors&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options28" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;If all eigenvalues are distinct&lt;/label&gt;&lt;/div&gt;
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                        &lt;p&gt;29. Which of the following is a property of a linear transformation?&lt;/p&gt;
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                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options29" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;T(u + v) = T(u) * T(v)&lt;/label&gt;&lt;/div&gt;
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                    &lt;!-- Question 30 --&gt;
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                        &lt;div class="question-info"&gt;
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                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
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                        &lt;p&gt;30. How is the characteristic polynomial of a matrix A defined?&lt;/p&gt;
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                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options30" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;It is the sum of the eigenvalues&lt;/label&gt;&lt;/div&gt;
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                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options30" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It is a polynomial of degree equal to the number of rows&lt;/label&gt;&lt;/div&gt;
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                if (adCloseButton) {
                    adCloseButton.style.display = 'inline';
                    console.log("Ad close button shown after 5 seconds.");
                }
            }, 5000);

            // Handle Ad Close Button
            if (adCloseButton) {
                adCloseButton.onclick = function () {
                    console.log("Ad close button clicked! Hiding ad modal.");
                    adModal.style.display = 'none';
                    document.getElementById('result-container').style.display = 'block';
                    displayResults();
                };
            }

            // Auto-close Ad after 10 seconds
            setTimeout(() =&gt; {
                if (adModal.style.display !== 'none') {
                    console.log("Ad auto-closing after 10 seconds.");
                    adModal.style.display = 'none';
                    document.getElementById('result-container').style.display = 'block';
                    showResult();
                }
            }, 10000);
        } else {
            console.error("Ad modal not found! Check HTML for id='adModal'");
        }

        // Stop timer
        clearInterval(timerInterval);
    };

    document.getElementById('cancelSubmit').onclick = function () {
        console.log("Cancel submit clicked! Closing modal.");
        modal.style.display = 'none';
        const fullscreenContainer = document.getElementById('fullscreen-container');

        // Request fullscreen again if necessary
        if (fullscreenContainer.requestFullscreen) {
            fullscreenContainer.requestFullscreen();
        }

        if (window.matchMedia("(orientation: portrait)").matches) {
            screen.orientation.lock("landscape").catch(function (error) {
                console.error("Orientation lock failed: ", error);
            });
        }
    };

    // Exit fullscreen mode
    const exitFullScreen =
        document.exitFullscreen ||
        document.mozCancelFullScreen ||
        document.webkitExitFullscreen ||
        document.msExitFullscreen;

    if (exitFullScreen) {
        exitFullScreen.call(document);
        console.log("Exited fullscreen.");
    }
};



        function displayResults() {
            document.getElementById('result-container').style.display = 'block';
            document.getElementById('user-name-display').innerText = userName;
            showResult();
            // window.location.href = './results.html'; 
        }

        document.getElementById('mark-for-review').onclick = function() {
            const subjectMarks = subjectData[currentSubject].markedForReview;
            const currentQuestion = questions[currentQuestionIndex];
            const userAnswer = getUserAnswer(currentQuestion);
            const fullscreenContainer = document.getElementById('fullscreen-container');
            fullscreenContainer.requestFullscreen();
            if (window.matchMedia("(orientation: portrait)").matches) {
                screen.orientation.lock("landscape").catch(function(error) {
                    console.error("Orientation lock failed: ", error);
                });
            }

            if (subjectMarks.has(currentQuestionIndex)) {
                subjectMarks.delete(currentQuestionIndex);
            } else {
                subjectMarks.add(currentQuestionIndex);
            }
            if (userAnswer) {
                subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
            } else {
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
            }
            updateQuestionPalette();
        }

        function handleQuestionStateBeforeChange() {
            const currentQuestion = questions[currentQuestionIndex];
            const userAnswer = getUserAnswer(currentQuestion);

            // Save the user's answer
            if (userAnswer) {
                subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
            } else {
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
            }

            // Always mark the question as seen
            markAsSeen(currentQuestionIndex);
        }

        function updateQuestionStats() {
            // Count answered questions (green buttons)
            const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'green').length;

            // Count marked for review questions (orange buttons)
            const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'orange').length;
            
            // Count marked for review questions (orange buttons)
            const AnsweredmarkedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'purple').length;

            // Total questions in the current subject
            const totalQuestions = questions.length;

            // Count unanswered questions (red buttons)
            const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'red').length;

            // Count not visited questions (black buttons)
            const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                .filter(button =&gt; button.style.backgroundColor === 'black').length;

            // Update the counts in the HTML
            document.getElementById('answered-count').textContent = `${answeredCount}`;
            document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
            document.getElementById('review-count').textContent = `${markedForReviewCount}`;
            document.getElementById('answered-review-count').textContent = `${AnsweredmarkedForReviewCount}`;
            document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
        }

        function updateQuestionPalette() {
            const palette = document.getElementById('question-palette');
            palette.innerHTML = '';
            palette.appendChild(document.createElement('br'));
            palette.appendChild(document.createElement('hr'));
            const subjectHeading = document.createElement('h3');
            subjectHeading.textContent = `${currentSubject} Questions`;
            palette.appendChild(subjectHeading);
            palette.appendChild(document.createElement('hr'));

            questions.forEach((question, index) =&gt; {
                const button = document.createElement('button');
                button.textContent = index + 1;
                button.classList.toggle('active', index === currentQuestionIndex);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }

                const subjectMarks = subjectData[currentSubject].markedForReview;
                const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                // Set button background color based on question state
                if (subjectMarks.has(index) &amp;&amp; subjectAnswered.has(index)) {
                    button.style.backgroundColor = 'purple'; // Answered and Marked for Review
                } else if (subjectAnswered.has(index)) {
                    button.style.backgroundColor = 'green'; // Answered
                } else if (subjectMarks.has(index)) {
                    button.style.backgroundColor = 'orange'; // Marked for Review
                } else if (questions[index].seen) {
                    button.style.backgroundColor = 'red'; // Unanswered
                } else {
                    button.style.backgroundColor = 'black'; // Not Visited
                }


                // Add event handler for question button
                button.onclick = () =&gt; {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex = index;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    updateQuestionStats(); // Update stats when changing questions
                };
                palette.appendChild(button);
            });

            updateQuestionStats(); // Update stats when rendering the palette
        }

        function markAsSeen(questionIndex) {
            questions[questionIndex].seen = true;
        }

        function startCountdown() {
            targetTime = Date.now() + countdownSeconds * 1000;
            updateTimerDisplay();
            timerInterval = setInterval(() =&gt; {
                if (Date.now() &gt;= targetTime) {
                    clearInterval(timerInterval);
                    document.getElementById('timer').textContent = "Time's Up!";
                    submitQuiz();
                } else {
                    updateTimerDisplay();
                }
            }, 1000);
        }

        function updateTimerDisplay() {
            const remainingTime = targetTime - Date.now();
            const minutes = Math.floor(remainingTime / 60000);
            const seconds = Math.floor((remainingTime % 60000) / 1000);
            document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
            if (remainingTime &lt; 600000) {
                document.getElementById('timer').style.color = 'red';
            } else {
                document.getElementById('timer').style.color = '';
            }
        }



        function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
            const userAnswerNum = parseFloat(userAnswer);
            const userDecimals = (userAnswer.split('.')[1] || '').length;
            const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;

            // Check if the answer has the correct number of decimal places
            const isCorrectPrecision = userDecimals === precision;

            return isInRange &amp;&amp; isCorrectPrecision;
        }

        function getUserAnswer(question) {
            const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
            const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
            const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
            return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
        }

        function addToInput(value) {
            // Get the current question's input field
            const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
            if (inputField) {
                inputField.value += value; // Append the value to the current input field
            }
        }

        function clearInput() {
            // Get the current question's input field
            const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
            if (inputField) {
                inputField.value = ''; // Clear the current input field
            }
        }

        function toggleSign() {
            // Get the current question's input field
            const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
            if (inputField) {
                if (inputField.value.startsWith('-')) {
                    inputField.value = inputField.value.substring(1); // Remove the negative sign
                } else {
                    inputField.value = '-' + inputField.value; // Add the negative sign
                }
            }
        }

        document.getElementById('restart').addEventListener('click', function() {
            // Reset quiz state
            currentQuestionIndex = 0;
            subjectData = {};
            timeTakenArray = {};

            // Show quiz
            document.getElementById('question-palette').style.display = 'block';

            // Call the function to start the quiz
            startQuiz();
        });

        function showResult() {
            const subjects = {};
            let totalScore = 0;
            const questions = document.querySelectorAll('.question');

            questions.forEach((question, i) =&gt; {
                const subject = question.getAttribute('data-subject');
                if (!subjects[subject]) {
                    subjects[subject] = {
                        correct: 0,
                        wrong: 0,
                        unattempted: 0,
                        score: 0,
                        timeSpent: 0,
                        questions: []
                    };
                }

                const questionType = question.getAttribute('data-type');
                const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                const userAnswer = getUserAnswer(question);
                const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                const optionElements = question.querySelectorAll('.options div label');
                const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());


                let questionDetail = {
                    questionText: question.querySelector('p').innerHTML,
                    userAnswer: userAnswer || 'Not answered',
                    correctAnswer: correctAnswer,
                    result: 'Wrong',
                    type: questionType,
                    correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                    incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                    options: options,
                    question: question,
                    explanation: explanation

                };
                evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                subjects[subject].questions.push(questionDetail);
                const timeSpent = timeTakenArray[subject][i] || 0;
                subjects[subject].timeSpent += parseFloat(timeSpent);
            });
            displayDetailedResults(subjects);
            displayDetailed(subjects);
            renderTimeSpentChart(subjects);
            checkUserPerformance(subjects);
        }

        function checkUserPerformance(subjects) {
            let totalScore = 0;
            let totalQuestions = 0;

            for (const subject in subjects) {
                totalScore += subjects[subject].score;
                totalQuestions += subjects[subject].questions.length;
            }

            const percentage = (totalScore / (totalQuestions * 1)) * 100;

            let message = '';
            if (percentage &gt; 60) {
                message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                showWinnerAnimation(message);
            } else if (percentage &gt;= 30) {
                message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                showFeedbackMessage(message);
            } else {
                message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                showFeedbackMessage(message);
            }
        }

        function showWinnerAnimation(message) {
            const winnerMessage = document.createElement('div');
            winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
            winnerMessage.style.position = 'fixed';
            winnerMessage.style.top = '50%';
            winnerMessage.style.left = '50%';
            winnerMessage.style.transform = 'translate(-50%, -50%)';
            winnerMessage.style.zIndex = '1000';
            winnerMessage.style.fontSize = '2em';
            winnerMessage.style.textAlign = 'center';
            document.body.appendChild(winnerMessage);

            // Animation effect
            winnerMessage.animate([{
                    transform: 'scale(1)',
                    opacity: 1
                },
                {
                    transform: 'scale(1.1)',
                    opacity: 1
                },
                {
                    transform: 'scale(1)',
                    opacity: 1
                }
            ], {
                duration: 1000,
                iterations: 3
            });

            // Remove the message after a few seconds
            setTimeout(() =&gt; {
                document.body.removeChild(winnerMessage);
            }, 10000);
        }

        function showFeedbackMessage(message) {
            const feedbackMessage = document.createElement('div');
            feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
            feedbackMessage.style.position = 'fixed';
            feedbackMessage.style.top = '50%';
            feedbackMessage.style.left = '50%';
            feedbackMessage.style.transform = 'translate(-50%, -50%)';
            feedbackMessage.style.zIndex = '1000';
            feedbackMessage.style.fontSize = '2em';
            feedbackMessage.style.textAlign = 'center';
            document.body.appendChild(feedbackMessage);

            // Remove the message after a few seconds
            setTimeout(() =&gt; {
                document.body.removeChild(feedbackMessage);
            }, 5000);
        }

        function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
            if (questionType === 'NAT') {
                const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                    questionDetail.result = 'Correct';
                    subjectStats.correct++;
                    subjectStats.score += questionDetail.correctScore;
                } else if (!userAnswer) {
                    questionDetail.result = 'Unattempted';
                    subjectStats.unattempted++;
                } else {
                    questionDetail.result = 'Wrong';
                    subjectStats.wrong++;
                    subjectStats.score += questionDetail.incorrectScore;
                }

                // Set the correct answer to be the range between dataMin and dataMax
                questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
            } else if (questionType === 'MCQ') {
                if (userAnswer === correctAnswer) {
                    questionDetail.result = 'Correct';
                    subjectStats.correct++;
                    subjectStats.score += questionDetail.correctScore;
                } else if (!userAnswer) {
                    questionDetail.result = 'Unattempted';
                    subjectStats.unattempted++;
                } else {
                    questionDetail.result = 'Wrong';
                    subjectStats.wrong++;
                    subjectStats.score += questionDetail.incorrectScore;
                }
            } else if (questionType === 'MSQ') {
                const correctAnswers = correctAnswer.split(';').sort().join(';');
                const userAnswers = userAnswer.split(';').sort().join(';');

                if (userAnswers === correctAnswers) {
                    questionDetail.result = 'Correct';
                    subjectStats.correct++;
                    subjectStats.score += questionDetail.correctScore;
                } else if (!userAnswer) {
                    questionDetail.result = 'Unattempted';
                    subjectStats.unattempted++;
                } else {
                    questionDetail.result = 'Wrong';
                    subjectStats.wrong++;
                    subjectStats.score += questionDetail.incorrectScore;
                }
                questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
            }
        }

        function displayDetailed(subjects) {
            const detailedResultsContainer = document.getElementById('detailed-results');
            detailedResultsContainer.innerHTML = ''; // Clear previous results

            for (const subject in subjects) {
                const subjectReport = subjects[subject];
                const subjectDiv = document.createElement('div');
                subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                let totalScore = 0; // Initialize total score

                subjectReport.questions.forEach((questionDetail, index) =&gt; {
                    const userAnswer = questionDetail.userAnswer;
                    const questionType = questionDetail.type; // Ensure question type is captured properly
                    const isCorrect = questionDetail.result === 'Correct';
                    const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                    const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                    let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                    let optionsHTML = '';

                    // Handle each question type properly
                    if (questionType === 'MCQ') {
                        optionsHTML = '&lt;div&gt;';
                        questionDetail.options.forEach((option) =&gt; {
                            const isChecked = userAnswer === option ? 'checked' : '';
                            optionsHTML +=
                                `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                        });
                        optionsHTML += '&lt;/div&gt;';
                    } else if (questionType === 'MSQ') {
                        optionsHTML = '&lt;div&gt;';
                        questionDetail.options.forEach((option) =&gt; {
                            const isChecked = userAnswer.includes(option) ? 'checked' : '';
                            optionsHTML +=
                                `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                        });
                        optionsHTML += '&lt;/div&gt;';
                    } else if (questionType === 'NAT') {
                        optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                    }

                    // Extract explanation from the question element
                    // const explanation = questionDetail.explanation || "No explanation available.";
                    // const explanation = question.getAttribute('data-explanation');

                    // Create HTML for question details
                    const questionHTML =
                        `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;          
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                    subjectDiv.innerHTML += questionHTML;

                    // Calculate the score based on the user's answers
                    const correctAnswers = questionDetail.correctAnswer.split(';');
                    const userAnswers = userAnswer.split(';');

                    if (isCorrect) {
                        totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                    } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                        totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                    } else {
                        totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                    }

                    // Insert the ad after every 3 questions
                    // if ((index + 1) % 1 === 0) {
                    //     const adDiv = document.createElement('div');
                    //     adDiv.id = 'adModel';
                    //     adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                    //     adDiv.style.border = '1px solid gray';
                    //     adDiv.style.padding = '10px';
                    //     adDiv.style.margin = '10px 0';
                    //     subjectDiv.appendChild(adDiv);
                    // } 
                    if ((index + 1) % 4 === 0) {
                        const adIns = document.createElement('ins');
                        adIns.className = 'adsbygoogle';
                        adIns.style.display = 'block';
                        adIns.setAttribute('data-ad-client', 'ca-pub-2922315402866630'); // your AdSense client ID
                        adIns.setAttribute('data-ad-slot', '4993484640'); // your AdSense ad slot ID
                        adIns.setAttribute('data-ad-format', 'auto');
                        adIns.setAttribute('data-full-width-responsive', 'true');

                        subjectDiv.appendChild(adIns);

                        // Defer push to next event loop to ensure element is in the DOM
                        setTimeout(() =&gt; {
                            try {
                                (adsbygoogle = window.adsbygoogle || []).push({});
                            } catch (e) {
                                console.error('AdSense error:', e);
                            }
                        }, 0);
                    }

                });
                detailedResultsContainer.appendChild(subjectDiv);
            }
        }

        /* function displayDetailedResults(subjects) {
            const resultBody = document.getElementById('result-body');
            resultBody.innerHTML = '';
            let totalScore = 0;
            let totalCorrect = 0;
            let totalWrong = 0;
            let totalUnattempted = 0;
            let totalTimeSpent = 0;

            for (const subject in subjects) {
                const subjectResult = subjects[subject];
                totalScore += subjectResult.score;
                totalCorrect += subjectResult.correct;
                totalWrong += subjectResult.wrong;
                totalUnattempted += subjectResult.unattempted;
                totalTimeSpent += subjectResult.timeSpent;

                // Subject summary row
                const subjectRow = `
                    &lt;tr class="category-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                        &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                        &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                        &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += subjectRow;
            }

            // Total summary row
            const totalRow = `
                &lt;tr class="total-row"&gt;
                    &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                    &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                    &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                    &lt;td&gt;${totalCorrect}&lt;/td&gt;
                    &lt;td&gt;${totalWrong}&lt;/td&gt;
                    &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                &lt;/tr&gt;
            `;
            resultBody.innerHTML += totalRow;
        } */

        function displayDetailedResults(subjects) {
            const resultBody = document.getElementById('result-body');
            resultBody.innerHTML = '';
            let totalScore = 0;
            let totalCorrect = 0;
            let totalWrong = 0;
            let totalUnattempted = 0;
            let totalTimeSpent = 0;

            for (const subject in subjects) {
                const subjectResult = subjects[subject];
                totalScore += subjectResult.score;
                totalCorrect += subjectResult.correct;
                totalWrong += subjectResult.wrong;
                totalUnattempted += subjectResult.unattempted;
                totalTimeSpent += subjectResult.timeSpent;

                // Convert time spent on the current subject to minutes and seconds
                const subjectMinutes = Math.floor(subjectResult.timeSpent / 60);
                const subjectSeconds = subjectResult.timeSpent % 60;

                // Ensure seconds are always two digits
                const formattedSubjectSeconds = subjectSeconds &lt; 10 ? `0${subjectSeconds}` : subjectSeconds;

                // Subject summary row
                const subjectRow = `
            &lt;tr class="category-row"&gt;
                &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                &lt;td&gt;${subjectMinutes.toString().padStart(2, '0')}min:${formattedSubjectSeconds}secs&lt;/td&gt;
                &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
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&lt;/html&gt;</description><link>https://aerogatetopper.blogspot.com/2024/10/linear-algebra-4.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-7088244005133698693</guid><pubDate>Mon, 28 Oct 2024 12:51:00 +0000</pubDate><atom:updated>2025-03-23T15:12:11.299+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Linear Algebra -3 </title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Linear Algebra Topic-wise Online Quiz&lt;/title&gt;
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          &lt;center&gt;&lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;&lt;/center&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
            &lt;p&gt;&lt;/p&gt;
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                &lt;li&gt;The total duration of the examination is 45 minutes .&lt;/li&gt;
                &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
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            &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;To answer a question, do the following:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;&lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;&lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;&lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;               
            &lt;li&gt;
            You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;&lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
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            Procedure for answering a numerical answer type question:&lt;/li&gt;
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                    &lt;!-- Question 1 --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;1. Given that the determinant of the matrix A is -12, what is the determinant of matrix B?
                        \[
                            A = \begin{pmatrix}
                            1 &amp; 3 &amp; 0 \\
                            2 &amp; 6 &amp; 4 \\
                            -1 &amp; 0 &amp; 2
                            \end{pmatrix}
                            \],
                            \[
                            B = \begin{pmatrix}
                            2 &amp; 6 &amp; 0 \\
                            4 &amp; 12 &amp; 8 \\
                            -2 &amp; 0 &amp; 4
                            \end{pmatrix}
                            \]&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options1" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;-96&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options1" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;-24&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options1" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;96&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options1" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;24&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 2 --&gt;
                    &lt;div class="question" data-answer="1" data-correct-score="2" data-incorrect-score="0" data-max="1" data-min="1" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation=""&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;2. A real (4x4) matrix A satisfies the equation A² = I, , where I is the (4 x4) identity matrix. The positive eigenvalue of A is______.&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer2" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;

                    &lt;/div&gt;

                    &lt;!-- Question 3 --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation=""&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;3. For matrices M, N and scalar C, which one of the following properties does NOT always hold?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options3" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;(CM)ᵀ = C(M)ᵀ&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options3" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;(Mᵀ)ᵀ = M&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options3" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;MN = NM&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options3" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;(M + N)ᵀ = Mᵀ + Nᵀ&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 4 --&gt;
                    &lt;div class="question" data-answer="1" data-max="1" data-min="1" data-precision="0" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="NAT" data-explanation=""&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;4. Consider the below matrix A. Which is obtained by reversing the order of the columns of the identity matrix I₆. Let P = I₆ + α * J₆, where α is non-negative real number. The value of α for which det(P) = 0 is _____.
                         \[
                        \begin{bmatrix}
                        0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 \\
                        0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 &amp; 0 \\
                        0 &amp; 0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 \\
                        0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 \\
                        0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
                        1 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
                        \end{bmatrix}
                        \]&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer4" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 5 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;5. Given the system of equations:
                            &lt;br&gt;x + 2y + 2z = b₁
                            &lt;br&gt;5x + y + 3z = b₂
                            &lt;br&gt;Which of the following is true regarding its solutions?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The system has a unique solution for any given b₁ and b₂&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The system will have infinitely many solutions for any given b₁ and b₂&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Whether or not a solution exists depends on b₁ and b₂&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The system would have no solution for any value of b₁ and b₂&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 6 --&gt;
                    &lt;div class="question" data-answer="3" data-max="3" data-min="3" data-precision="0" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="NAT"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;6. A system matrix is given as follows. The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is ___.
                        \[
                            A = \begin{pmatrix}
                            0 &amp; 1 &amp; -1 \\
                            -6 &amp; -11 &amp; 6 \\
                            -6 &amp; -11 &amp; 5
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer6" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 7 --&gt;
                    &lt;div class="question" data-answer="2" data-max="2" data-min="2" data-precision="0" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="NAT" data-explanation=""&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;7. If 1, 0, and -1 are the eigenvalues of a 3×3 matrix A, then the trace of A^2 + 5A is equal to ___&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer7" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 8 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation=""&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;8. For the matrix,
                         \[
                            M = \begin{pmatrix}
                            1 &amp; 0 &amp; -1 \\
                            0 &amp; 1 &amp; -1 \\
                            1 &amp; 1 &amp; -2
                            \end{pmatrix}
                            \]
                        consider the following statements:
                        &lt;br&gt;(P) the characteristic equation of M is λ^3-λ =0.
                        &lt;br&gt;(Q) M^-1 Does not exist.
                        &lt;br&gt;(R) The matrix M is Diagonalizable.&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;P and R but not Q&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;P and Q but not R&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;P, Q, and R&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;&lt;label for="mcq-option3"&gt;P, Q, and R&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 9 --&gt;
                    &lt;div class="question" data-answer="5" data-max="5" data-min="5" data-precision="0" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="NAT" data-explanation=""&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;9. Let A be an (m×n) matrix and B be an (n×m) matrix. It is given that determinant(I&lt;sub&gt;m&lt;/sub&gt; + AB) = determinant(I&lt;sub&gt;n&lt;/sub&gt; + BA), where I&lt;sub&gt;k&lt;/sub&gt; is the k×k identity matrix. Using the above property, the determinant of the matrix below is ___&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer9" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 10 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;10. Let r and s be real numbers. If then the system of linear equations AX = b has
                        \[
                            A = \begin{pmatrix}
                            1 &amp; 2 &amp; 0 \\
                            2 &amp; 0 &amp; 3 \\
                            r &amp; s &amp; 0
                            \end{pmatrix}
                            \]
                            and, \[
                            b = \begin{pmatrix}
                            1 \\
                            1 \\
                            s-1 
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options10" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;A unique solution for s = 2r = 2&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options10" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Infinitely many solutions for s = 2r = 2&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options10" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Infinitely many solutions for s = 2r ≠ 2&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options10" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;No solution for s ≠ 2r &lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 11 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;11. &lt;p&gt;Matrix A and one of its normalized eigenvectors:&lt;/p&gt;
                        &lt;p&gt;A = 
                            \[
                            \begin{pmatrix}
                            5 &amp; 3 \\
                            1 &amp; 3
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;p&gt;One of the normalized Eigen vectors is given as:&lt;/p&gt;

                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options11" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;\[
                            \begin{pmatrix}
                            1 \\
                            2 \\
                            \sqrt{3}/2
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options11" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;\[
                            \begin{pmatrix}
                            1/\sqrt{2} \\
                            -1/\sqrt{2}
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options11" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;\[
                            \begin{pmatrix}
                            3/\sqrt{10} \\
                            -1/\sqrt{10}
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options11" type="radio" value="C" /&gt;&lt;label for="mcq-option4"&gt;\[
                            \begin{pmatrix}
                            1/\sqrt{5} \\
                            2/\sqrt{5}
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 12 --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
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                        &lt;/div&gt;
                        &lt;p&gt;12.&lt;br&gt;x + 2y + z = 4
                            &lt;br&gt;2x + y + 2z = 5
                            &lt;br&gt;x - y + z = 1
                            &lt;br&gt;The system of algebraic equations given above has ___ solutions:&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options12" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;No feasible solution&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options12" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Infinite number of solutions&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options12" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Only the two solutions of (x=1,y=1,z=1) and (x=2, y=1, z=0).&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options12" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;A unique solution of x=1, y=1 and z=1&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 13 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
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                        &lt;/div&gt;
                        &lt;p&gt;13. Given that
                        \[
                            A = \begin{pmatrix}
                            -5 &amp; -3 \\
                            2 &amp; 0
                            \end{pmatrix}
                            \] and \[
                            I = \begin{pmatrix}
                            1 &amp; 0 \\
                            0 &amp; 1
                            \end{pmatrix}
                            \]
                            the value of A^3 is
                        &lt;/p&gt;
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                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options13" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;17A + 21I&lt;/label&gt;&lt;/div&gt;
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                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options13" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;15A + 12I&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options13" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;19A + 30I&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 14 --&gt;
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                        &lt;div class="question-info"&gt;
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                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;14. The minimum eigenvalue of the following matrix is

                        \[
                            \begin{pmatrix}
                            3 &amp; 5 &amp; 2 \\
                            5 &amp; 12 &amp; 7 \\
                            2 &amp; 7 &amp; 5
                            \end{pmatrix}
                            \]

                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer14" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 15 --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ"&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;15. A matrix has eigenvalues -1 and -2. 
                        The corresponding eigen vectors are \[
                            \begin{pmatrix}
                            1 \\
                            -1
                            \end{pmatrix}
                            \]
                            and \[
                            \begin{pmatrix}
                            1 \\
                            -2 
                            \end{pmatrix}
                            \]
                            respectively. The matrix is?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt; \[
                        \begin{pmatrix}
                            1 &amp; 1 \\
                            -1 &amp; -2
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options15" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;\[
                        \begin{pmatrix}
                            1 &amp; 2 \\
                            -2 &amp; -4
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;\[
                        \begin{pmatrix}
                            -1 &amp; 0 \\
                            0 &amp; -2
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;\[
                        \begin{pmatrix}
                            0 &amp; 1 \\
                            -2 &amp; -3
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;


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            document.getElementById('clear').onclick = function(){
                const currentQuestion = questions[currentQuestionIndex];
                currentQuestion.querySelectorAll('input:checked').forEach(input =&gt; input.checked = false);
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
              	if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                
                updateQuestionPalette();
            }

            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestionIndex];
                const timeTaken = (questionEndTime - questionStartTime) / 1000;
                const subject = currentSubject;            
                if (!timeTakenArray[subject]) {
                    timeTakenArray[subject] = {};
                }
                if (!timeTakenArray[subject][currentQuestionIndex]) {
                    timeTakenArray[subject][currentQuestionIndex] = 0;
                }
                timeTakenArray[subject][currentQuestionIndex] += timeTaken;
                questionStartTimes[currentQuestionIndex] = questionEndTime;
            }

            document.getElementById('submit').onclick = function(){
                recordTimeTaken();
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';    
                document.getElementById('confirmSubmit').onclick = function() {
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    modal.style.display = 'none';    
                    const adModal = document.getElementById('adModal');
                    const adCloseButton = document.getElementById('adClose');
                    adModal.style.display = 'block';    
                    setTimeout(() =&gt; {
                        adCloseButton.style.display = 'inline';
                    }, 5000);    
                    adCloseButton.onclick = function() {
                        adModal.style.display = 'none';
                        displayResults(); // Ensure this function is called to show results
                    };    
                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block'; // Show result container
                            showResult(); // Ensure this function is called to show results
                        }
                    }, 10000);    
                    clearInterval(timerInterval);
                };    
                document.getElementById('cancelSubmit').onclick = function() {
                    modal.style.display = 'none';
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                };    
                const exitFullScreen = document.exitFullscreen || document.mozCancelFullScreen || document.webkitExitFullscreen || document.msExitFullscreen;
                if (exitFullScreen) exitFullScreen.call(document);
            }

            function displayResults() {
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('user-name-display').innerText = userName;
                showResult();
                // window.location.href = './results.html'; 
            }

            document.getElementById('mark-for-review').onclick = function()  {
                const subjectMarks = subjectData[currentSubject].markedForReview;
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
              	if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                       	console.error("Orientation lock failed: ", error);
                   	});
               	}

                if (subjectMarks.has(currentQuestionIndex)) {
                    subjectMarks.delete(currentQuestionIndex);
                } else {
                    subjectMarks.add(currentQuestionIndex);
                }
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }
                updateQuestionPalette();
            }

            function handleQuestionStateBeforeChange() {
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);

                // Save the user's answer
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }

                // Always mark the question as seen
                markAsSeen(currentQuestionIndex);
            }

            function updateQuestionStats() {
                // Count answered questions (green buttons)
                const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'green').length;

                // Count marked for review questions (orange buttons)
                const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'orange').length;

                // Total questions in the current subject
                const totalQuestions = questions.length;

                // Count unanswered questions (red buttons)
                const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'red').length;

                // Count not visited questions (black buttons)
                const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'black').length;

                // Update the counts in the HTML
                document.getElementById('answered-count').textContent = `${answeredCount}`;
                document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
                document.getElementById('review-count').textContent = `${markedForReviewCount}`;
                document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
            }

            function updateQuestionPalette() {
                const palette = document.getElementById('question-palette');
                palette.innerHTML = '';
                palette.appendChild(document.createElement('br'));
                palette.appendChild(document.createElement('hr'));
                const subjectHeading = document.createElement('h3');
                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  	if (window.matchMedia("(orientation: portrait)").matches) {
                    	screen.orientation.lock("landscape").catch(function(error) {
                        	console.error("Orientation lock failed: ", error);
                    	});
                	}

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            /* function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            } */

            function displayDetailedResults(subjects) {
    const resultBody = document.getElementById('result-body');
    resultBody.innerHTML = '';
    let totalScore = 0;
    let totalCorrect = 0;
    let totalWrong = 0;
    let totalUnattempted = 0;
    let totalTimeSpent = 0;

    for (const subject in subjects) {
        const subjectResult = subjects[subject];
        totalScore += subjectResult.score;
        totalCorrect += subjectResult.correct;
        totalWrong += subjectResult.wrong;
        totalUnattempted += subjectResult.unattempted;
        totalTimeSpent += subjectResult.timeSpent;

        // Convert time spent on the current subject to minutes and seconds
        const subjectMinutes = Math.floor(subjectResult.timeSpent / 60);
        const subjectSeconds = subjectResult.timeSpent % 60;

        // Ensure seconds are always two digits
        const formattedSubjectSeconds = subjectSeconds &lt; 10 ? `0${subjectSeconds}` : subjectSeconds;

        // Subject summary row
        const subjectRow = `
            &lt;tr class="category-row"&gt;
                &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                &lt;td&gt;${subjectMinutes.toString().padStart(2, '0')}min:${formattedSubjectSeconds}secs&lt;/td&gt;
                &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
            &lt;/tr&gt;
        `;
        resultBody.innerHTML += subjectRow;
    }

    // Convert totalTimeSpent (in seconds) to minutes and seconds
    const totalMinutes = Math.floor(totalTimeSpent / 60);
    const totalSeconds = totalTimeSpent % 60;

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            &lt;td&gt;${totalMinutes.toString().padStart(2, '0')}min:${formattedTotalSeconds}secs&lt;/td&gt;
            &lt;td&gt;${totalCorrect}&lt;/td&gt;
            &lt;td&gt;${totalWrong}&lt;/td&gt;
            &lt;td&gt;${totalUnattempted}&lt;/td&gt;
        &lt;/tr&gt;
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}

            
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                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
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            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/linear-algebra-3.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-2458286195860546296</guid><pubDate>Mon, 28 Oct 2024 12:49:00 +0000</pubDate><atom:updated>2025-03-23T15:12:48.938+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Linear Algebra-2 </title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Linear Algebra Topic-wise Online Quiz&lt;/title&gt;
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        &lt;div id="user-info"&gt;
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          &lt;center&gt;&lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;&lt;/center&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
            &lt;p&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;
                &lt;li&gt;The total duration of the examination is 45 minutes .&lt;/li&gt;
                &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
                &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
            &lt;/ol&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;To answer a question, do the following:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;&lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;&lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;&lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;               
            &lt;li&gt;
            You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;&lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To select your answer, click on the button on one of the options&lt;/li&gt;&lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;&lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next &lt;/b&gt;button&lt;/li&gt;&lt;/ol&gt;&lt;li&gt;
            Procedure for answering a numerical answer type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;&lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;&lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;&lt;/ol&gt;  
            &lt;li&gt;
            To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;&lt;/ol&gt;&lt;ol style="text-align: left;"&gt;
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            &lt;center&gt;&lt;button id="start-button"&gt;Start Quiz&lt;/button&gt;&lt;/center&gt;
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                &lt;p&gt;Do you really want to submit this quiz?&lt;/p&gt;
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                    &lt;!-- Question 1 (NAT - Tough) --&gt;
                    &lt;div class="question" data-answer="2" data-correct-score="1" data-incorrect-score="0" data-max="2" data-min="2" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="To find the rank of a matrix, we perform row reduction to bring it to row echelon form. The rank is the number of non-zero rows in this form."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;1. Find the rank of the matrix:
                            \[
                            A = \begin{pmatrix}
                            1 &amp; 2 &amp; 3 &amp; 4 \\
                            2 &amp; 4 &amp; 6 &amp; 8 \\
                            1 &amp; 1 &amp; 1 &amp; 1 \\
                            3 &amp; 5 &amp; 7 &amp; 9
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer1" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 2 (MCQ - Tough) --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="To find the eigenvalues of a matrix, solve the characteristic equation |A - λI| = 0. The roots of this equation give the eigenvalues."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;2. Which of the following is an eigenvalue of the matrix 
                            \[
                            B = \begin{pmatrix}
                            3 &amp; 1 \\
                            0 &amp; 2
                            \end{pmatrix}
                            \]?
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;4&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;1&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options2" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;3&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;0&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 3 (NAT - Tough) --&gt;
                    &lt;div class="question" data-answer="2" data-correct-score="2" data-incorrect-score="0" data-max="2" data-min="2" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="To solve a system of linear equations using matrices, we reduce the augmented matrix to row echelon form and determine the number of free variables."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;3. How many free variables are present in the system of equations represented by the matrix:
                            \[
                            \begin{pmatrix}
                            1 &amp; 2 &amp; 3 &amp; | &amp; 4 \\
                            0 &amp; 1 &amp; 4 &amp; | &amp; 5 \\
                            0 &amp; 0 &amp; 1 &amp; | &amp; 1
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer3" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 4 (MCQ - Tough) --&gt;
                    &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="For diagonalizable matrices, A = PDP⁻¹, where D is a diagonal matrix containing the eigenvalues of A, and P contains the corresponding eigenvectors."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;4. A matrix A is diagonalizable if:
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options4" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;All eigenvalues are real&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options4" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;A has linearly independent eigenvectors&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options4" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;All eigenvalues are distinct&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options4" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;A is symmetric&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 5 (NAT - Tough) --&gt;
                    &lt;div class="question" data-answer="71" data-correct-score="1" data-incorrect-score="0" data-max="71" data-min="71" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="To find the determinant of a matrix, apply cofactor expansion or use properties like row reduction to simplify the calculation."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;5. Calculate the determinant of the matrix:
                            \[
                            C = \begin{pmatrix}
                            4 &amp; 1 &amp; 2 \\
                            0 &amp; 3 &amp; 5 \\
                            1 &amp; 0 &amp; 6
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer5" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;



                    &lt;!-- Question 6 (NAT - Very Tough) --&gt;
                    &lt;div class="question" data-answer="1" data-correct-score="2" data-incorrect-score="0" data-max="1" data-min="1" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="The geometric multiplicity of an eigenvalue is the dimension of its eigenspace, and it is found by solving (A - λI)v = 0, where λ is the eigenvalue."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;6. Find the geometric multiplicity of the eigenvalue λ = 3 for the matrix:
                            \[
                            A = \begin{pmatrix}
                            3 &amp; 1 &amp; 0 \\
                            0 &amp; 3 &amp; 1 \\
                            0 &amp; 0 &amp; 3
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer6" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 7 (MCQ - Very Tough) --&gt;
                    &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="To find the inverse of a matrix, we use the adjugate and determinant. A matrix is invertible if and only if its determinant is non-zero."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;7. Which of the following matrices is not invertible?
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options7" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;\[
                            \begin{pmatrix}
                            1 &amp; 2 \\
                            3 &amp; 4
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options7" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;\[
                            \begin{pmatrix}
                            2 &amp; -1 \\
                            4 &amp; 2
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options7" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;\[
                            \begin{pmatrix}
                            0 &amp; 1 \\
                            1 &amp; 0
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options7" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;\[
                            \begin{pmatrix}
                            1 &amp; 1 \\
                            2 &amp; 2
                            \end{pmatrix}
                            \]&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 8 (NAT - Very Tough) --&gt;
                    &lt;div class="question" data-answer="6" data-correct-score="1" data-incorrect-score="0" data-max="6" data-min="6" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="The trace of a matrix is the sum of its diagonal elements, which is also equal to the sum of its eigenvalues."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;8. Calculate the trace of the matrix:
                            \[
                            A = \begin{pmatrix}
                            2 &amp; 1 &amp; 0 \\
                            0 &amp; 3 &amp; 1 \\
                            0 &amp; 0 &amp; 1
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer8" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 9 (MCQ - UPSC Tough) --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Cayley-Hamilton theorem states that every square matrix satisfies its own characteristic equation."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;9. Which theorem states that every square matrix satisfies its own characteristic equation?
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options9" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Gram-Schmidt process&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options9" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Rank-nullity theorem&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options9" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Cayley-Hamilton theorem&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options9" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Gauss-Jordan elimination&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 10 (NAT - UPSC Tough) --&gt;
                    &lt;div class="question" data-answer="4" data-correct-score="1" data-incorrect-score="0" data-max="4" data-min="4" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="The dimension of the null space of a matrix is called its nullity. It can be found by subtracting the rank of the matrix from the number of columns."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;10. A matrix has 6 columns and a rank of 2. Calculate the nullity of the matrix.
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer10" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 11 (NAT - UPSC Tough) --&gt;
                    &lt;div class="question" data-answer="0" data-correct-score="1" data-incorrect-score="0" data-max="0" data-min="0" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="The determinant of a matrix is zero if the rows or columns of the matrix are linearly dependent."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;11. Find the determinant of the following matrix:
                            \[
                            A = \begin{pmatrix}
                            1 &amp; 2 &amp; 3 \\
                            2 &amp; 4 &amp; 6 \\
                            3 &amp; 6 &amp; 9
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer11" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 12 (MCQ - UPSC Tough) --&gt;
                    &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Gram-Schmidt process is used to convert a set of linearly independent vectors into an orthonormal set."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;12. Which process is used to orthogonalize a set of vectors in an inner product space?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options12" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Gram-Schmidt process&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options12" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Gaussian elimination&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options12" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;QR decomposition&lt;/label&gt;&lt;/div&gt;
                            &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options12" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;LU decomposition&lt;/label&gt;&lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 13 (NAT - UPSC Tough) --&gt;
                    &lt;div class="question" data-answer="1" data-correct-score="1" data-incorrect-score="0" data-max="1" data-min="1" data-precision="0" data-subject="Linear Algebra" data-type="NAT" data-explanation="The rank of a matrix is the number of non-zero rows in its row echelon form."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;13. Find the rank of the matrix:
                            \[
                            B = \begin{pmatrix}
                            1 &amp; 0 &amp; 1 \\
                            2 &amp; 0 &amp; 2 \\
                            3 &amp; 0 &amp; 3
                            \end{pmatrix}
                            \]
                        &lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;input id="nat-answer13" name="nat-options" type="text" /&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;!-- Question 14 (MCQ - UPSC Tough) --&gt;
                    &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The nullity of a matrix is equal to the number of free variables, which is the total number of variables minus the rank of the matrix."&gt;
                        &lt;div class="question-info"&gt;
                            &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                            &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                        &lt;/div&gt;
                        &lt;p&gt;14. If a matrix has 5 columns and rank 3, what is its nullity?&lt;/p&gt;
                        &lt;div class="options"&gt;
                            &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options14" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;5&lt;/label&gt;&lt;/div&gt;
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                        &lt;p&gt;15. Is the matrix 
                            \[
                            C = \begin{pmatrix}
                            1 &amp; 2 \\
                            2 &amp; 4
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            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            /* function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            } */

            function displayDetailedResults(subjects) {
    const resultBody = document.getElementById('result-body');
    resultBody.innerHTML = '';
    let totalScore = 0;
    let totalCorrect = 0;
    let totalWrong = 0;
    let totalUnattempted = 0;
    let totalTimeSpent = 0;

    for (const subject in subjects) {
        const subjectResult = subjects[subject];
        totalScore += subjectResult.score;
        totalCorrect += subjectResult.correct;
        totalWrong += subjectResult.wrong;
        totalUnattempted += subjectResult.unattempted;
        totalTimeSpent += subjectResult.timeSpent;

        // Convert time spent on the current subject to minutes and seconds
        const subjectMinutes = Math.floor(subjectResult.timeSpent / 60);
        const subjectSeconds = subjectResult.timeSpent % 60;

        // Ensure seconds are always two digits
        const formattedSubjectSeconds = subjectSeconds &lt; 10 ? `0${subjectSeconds}` : subjectSeconds;

        // Subject summary row
        const subjectRow = `
            &lt;tr class="category-row"&gt;
                &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                &lt;td&gt;${subjectMinutes.toString().padStart(2, '0')}min:${formattedSubjectSeconds}secs&lt;/td&gt;
                &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
            &lt;/tr&gt;
        `;
        resultBody.innerHTML += subjectRow;
    }

    // Convert totalTimeSpent (in seconds) to minutes and seconds
    const totalMinutes = Math.floor(totalTimeSpent / 60);
    const totalSeconds = totalTimeSpent % 60;

    // Ensure total seconds are always two digits
    const formattedTotalSeconds = totalSeconds &lt; 10 ? `0${totalSeconds}` : totalSeconds;

    // Total summary row
    const totalRow = `
        &lt;tr class="total-row"&gt;
            &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
            &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
            &lt;td&gt;${totalMinutes.toString().padStart(2, '0')}min:${formattedTotalSeconds}secs&lt;/td&gt;
            &lt;td&gt;${totalCorrect}&lt;/td&gt;
            &lt;td&gt;${totalWrong}&lt;/td&gt;
            &lt;td&gt;${totalUnattempted}&lt;/td&gt;
        &lt;/tr&gt;
    `;
    resultBody.innerHTML += totalRow;
}

            
            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/linear-algebra-2.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-4381562471759404348</guid><pubDate>Mon, 28 Oct 2024 12:46:00 +0000</pubDate><atom:updated>2025-03-23T15:13:26.902+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Linear Algebra - 1</title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Linear Algebra Topic-wise Online Quiz&lt;/title&gt;
      &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
        &lt;!-- &lt;link href="quiz.css" rel="stylesheet"&gt; --&gt;
        &lt;meta charset="UTF-8"&gt;&lt;/meta&gt;
        &lt;meta content="width=device-width, initial-scale=1.0" name="viewport"&gt;&lt;/meta&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        
        &lt;style&gt;
          .col-lg-3{
            display:none;
          }
          .col-lg-9{
            flex: 0 0 100%;
          }
            .container{
	            padding:5px;
            }

            img{
            
            border:0px;
            }
            /* .options{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            } */
            .options div{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            }

            #question-container{
            
                padding:4px;
                height:35%;
                overflow-y:auto;
                padding-bottom: 100px;
                
            }
            
            #footer_buttons{
                display: none;
                position:fixed;
                bottom:0px;
                background:#ffffff;
                width:100%;
                height:80px;
                padding:4px;		
                border-top:1px solid #dddddd;
            }
            /* .question-info{
                margin: 5px auto;
                padding: 5px 0px 20px;
                border-bottom: 1px solid #CECECE;
                overflow-y: auto;
            } */
            #fullscreen-container row{
                margin-right: -15px;
                margin-left: -15px;
                display: flex;
                gap:15px;
                width: 100%;
            }
            #fullscreen-container row col-md-8, col-md-4{
                position: relative;
                min-height: 1px;
                padding-left: 15px;
                padding-right: 15px;
            }
            #fullscreen-container row col-md-8{
                float:left;
                width: 66.66666667%;
            }
            #fullscreen-container  row col-md-4{
                float:right;
                width: 33.33333333%;
            }
            .container-fluid{
                padding-left: 15px;
                padding-right: 15px;
                margin-left: auto;
                margin-right: auto;
            }
            #fullscreen-container{
                display: none;
                background-color: #ffffff;
                overflow: auto;
            }
            .quiz-attempt-inline-block{
                display: inline-block;
                width: 180px;
            }
         	#fullscreen-container .question-palette button {
              width: 40px;
              margin: 5px;
              padding: 5px;
            }
            @media(max-width:900px){
               #fullscreen-container button #confirmSubmit #cancelSubmit #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                gap:10px;
                font-size: 12px;
            }
                #fullscreen-container .row .col-md-4 .col-md-8 .options{
                    font-size: 12px;
                }
                #fullscreen-container .col-md-4{
                    width: 33.33333333%;
                }
                #fullscreen-container .col-md-8{
                    width: 66.66666667%;
                }
                 #fullscreen-container #footer_buttons{
                    bottom:0px;
                  	height:auto;
                }

                #fullscreen-container.quiz-attempt-inline-block{
                    display: flex;
                }
                #answered-count, #unanswered-count,#review-count,#not-visited-count {
                    width:20px;
                    margin: 5px;
                    padding: 5px;
                }
                #fullscreen-container h1 p{
                    font-size: 12px;
                }
              
                #fullscreen-container .question-palette h3{
                  font-size:14px;
                  font-weight:bold;
                }
                #calc-container {
                  position: absolute;
                  top: 30%;
                  left: 50%;
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            }

            .angled-text {
                text-align: center;
                transform: rotate(-45deg);
                font-size: 44px;
                font-weight: bolder;
                color: rgba(19, 17, 17, 0.352);
                z-index: 1;
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        &lt;/style&gt;

        &lt;style&gt;
            body {
                font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
                margin: 0;
                padding: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #333;
                background-color: #f2f2f2;
            }

            /* #cont, #quiz-container, #container {
                background-color: #fff;
            }

            #cont {
                overflow: auto;
                height: 100vh;
                flex-wrap: wrap;
                flex-direction: row;
            } */
/* 
            .question {
                margin-top: 10px;
                padding: 10px;
                overflow-y: auto;
                display: none;
                width: 70%;
                margin-bottom: 20px;
            } */

            h1, p {
                font-size: 16px;
                margin-top: 20px;
                color: #333;
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            .options {
                display: flex;
                flex-direction: column;
                flex-wrap: wrap;
                gap: 10px;
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            .options div {
                display: flex;
                align-items: center;
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            label {
                margin-left: 5px;
                font-size: 14px;
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            input[type="radio"], input[type="checkbox"] {
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                transition: background-color 0.3s ease;
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            button:hover, #submit-user-info:hover {
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            #cancelSubmit:hover {
                background-color: #d43f3a;
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            #clear, #prev, #next, #mark-for-review, #submit {
                padding: 10px 20px;
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            #prev, #next {
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            #prev:hover, #next:hover {
                background-color: #4cae4c;
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            #mark-for-review {
                background-color: #f0ad4e;
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            #submit {
                background-color: #d9534f;
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            #submit:hover {
                background-color: #d43f3a;
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            /* #result {
                text-align: center;
                font-size: 20px;
                font-weight: bold;
                margin-top: 20px;
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            #score-summary {
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            #score-summary tbody tr:nth-child(odd) {
                background-color: #f9f9f9;
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            #score-summary tbody tr:hover {
                background-color: #e0e0e0;
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            #user-info {
                max-width: 400px;
                margin: 0 auto;
                padding: 20px;
                background-color: #f9f9f9;
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            #user-info input[type="text"], #user-info input[type="email"] {
                width: 90%;
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            #user-info input[type="text"]:focus, #user-info input[type="email"]:focus {
                border-color: #007bff;
                box-shadow: 0 0 5px rgba(0, 123, 255, 0.5);
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            .question-palette {
                background-color: #fff;
            }

            .question-palette button {
                margin: 10px;
                padding: 10px;
                border: 1px solid #ccc;
                background-color: black;
                color: white;
            }

            .correct-answer {
                background-color: #71ba5d;
                color: white;
            }

            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
            }

            .not-answered {
                background-color: #fff;
                color: black;
            }

            table {
                width: 100%;
                border-collapse: collapse;
                margin-bottom: 20px;
            }

            th, td {
                border: 1px solid #ddd;
                padding: 8px;
            }

            th {
                background-color: #f2f2f2;
                text-align: left;
                font-weight: bold;
            }

            .category-row {
                background-color: #e0f7fa; /* Light cyan */
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            .total-row {
                background-color: #ffe0b2; /* Light orange */
            }

            .modal, .admodal {
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
                top: 0;
                width: 100%;
                height: 100%;
                background-color: rgba(0, 0, 0, 0.4);
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            .modal-content, .admodal-content {
                background-color: white;
                margin: 15% auto;
                padding: 20px;
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            .adclose {
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                float: right;
                font-size: 28px;
                font-weight: bold;
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            .adclose:hover, .adclose:focus {
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            #start-page {
                display: none;
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            #start-button {
                display: inline-block;
                padding: 10px;
                font-size: 18px;
                background-color: #007bff;
                color: #fff;
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              #numeric-keypad {                
                margin-top:50px;
                background-color: #f9f9f9;
                box-shadow: 0 -2px 10px rgba(0, 0, 0, 0.2);
                padding: 10px; 
                z-index: 1000;
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              #numeric-keypad .options {
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              #numeric-keypad h3 {
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              #numeric-keypad div {
                  display: flex;
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                  margin-bottom: 5px;
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              #numeric-keypad button {
                  background-color: #4185f2;
                width:30px;
                  color: white;
                  border: none;
                  border-radius: 5px;
                  padding: 10px;
                  font-size: 15px;
                  margin: 0 5px;
                  cursor: pointer;
                  transition: background-color 0.3s;
              }

              #numeric-keypad button:hover {
                  background-color: #0056b3;
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              #numeric-keypad button:active {
                  background-color: #004080;
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            @media screen and (max-width: 900px) {
                body, p, label {
                    font-size: 14px;
                }

                .question-palette button {
                    text-align: center;
                }
            }
            .question-info {
                display: flex;
                flex-direction: column;
                gap: 10px; /* Adjust the spacing between elements */
            }

            #calc-container {
                  position: absolute;
                  top: 30%;
                  margin-left: 50%;
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            #detailed-results .question-result{
              padding:30px;
              border: 2px solid black;
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            #detailed-results{
              left: 20px; 
              padding:20px;
            }
            #detailed-results h3{
            text-align:center; 
            font-size:25px; 
            font-weight:bold;
            }
        &lt;/style&gt;
    &lt;/head&gt;
    &lt;body&gt;
        &lt;div id="user-info"&gt;
          &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
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                (adsbygoogle = window.adsbygoogle || []).push({});
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            &lt;form id="registrationForm"&gt;            
                &lt;h1&gt;Enter Your Details&lt;/h1&gt;
               	&lt;input type="hidden" id="password" name="password" value="Linear Algebra - 1" /&gt;
                &lt;label for="name"&gt;Name:&lt;/label&gt;
                &lt;input id="username" name="username" required="" type="text" /&gt;
                &lt;!-- &lt;label for="email"&gt;Email:&lt;/label&gt;
                &lt;input id="email" name="email" required="" type="email" /&gt; --&gt;
                &lt;button type="submit" id="submit-user-info"&gt;Next&lt;/button&gt;
            &lt;/form&gt;
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            &lt;/script&gt;
        &lt;/div&gt;
      
        &lt;div id="start-page" style="display: none;"&gt;
          &lt;center&gt;&lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;&lt;/center&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
            &lt;p&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;
                &lt;li&gt;The total duration of the examination is 45 minutes .&lt;/li&gt;
                &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
                &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
            &lt;/ol&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;To answer a question, do the following:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;&lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;&lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;&lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;               
            &lt;li&gt;
            You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;&lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To select your answer, click on the button on one of the options&lt;/li&gt;&lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;&lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next &lt;/b&gt;button&lt;/li&gt;&lt;/ol&gt;&lt;li&gt;
            Procedure for answering a numerical answer type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;&lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;&lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;&lt;/ol&gt;  
            &lt;li&gt;
            To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;&lt;/ol&gt;&lt;ol style="text-align: left;"&gt;
            &lt;/ol&gt;
            &lt;center&gt;&lt;button id="start-button"&gt;Start Quiz&lt;/button&gt;&lt;/center&gt;
        &lt;/div&gt;

        &lt;div class="modal" id="myModal" style="display: none;"&gt;
            &lt;div class="modal-content"&gt;
                &lt;h2&gt;Quiz Submission Confirmation&lt;/h2&gt;
                &lt;p&gt;Do you really want to submit this quiz?&lt;/p&gt;
                &lt;button id="confirmSubmit"&gt;Submit Quiz&lt;/button&gt;
                &lt;button id="cancelSubmit"&gt;Cancel&lt;/button&gt;
            &lt;/div&gt;
        &lt;/div&gt;

        &lt;div class="admodal" id="adModal" style="display: none;"&gt;
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        &lt;div id="fullscreen-container" style="display: none;"&gt;
            &lt;div class="container-fluid"&gt;
                &lt;div class="row" id="container" style="display: flex;"&gt;
                    &lt;div class="col-md-8" id="quiz-container" style="width: 66.666666%;"&gt;                        
                        &lt;div class="category-calculator"&gt;
                            &lt;div class="quiz-attempt-title" style="float: left; width: 33.333333%;"&gt;
                                &lt;p&gt;Linear Algebra&lt;/p&gt;
                            &lt;/div&gt;
                            &lt;div class="calc" style="float: right;"&gt;
                                &lt;button class="btn-sm btn-info" id="calc-btn" onclick="$('#calc').window('open');"&gt;Calculator &lt;/button&gt;
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                        &lt;div style="clear: both;"&gt;&lt;/div&gt;

                        &lt;div class="quiz-timer" style="text-align: right;"&gt;
                            &lt;b&gt;Time Left:
                                &lt;span id="timer"&gt;000:00&lt;/span&gt;
                            &lt;/b&gt;
                        &lt;/div&gt;
                        &lt;hr /&gt;

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                            &lt;!-- &lt;button onclick="showSubject('Aptitude')"&gt;General Aptitude&lt;/button&gt; --&gt;
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                        &lt;div class="quiz-attempt-logo" style="display:flex; margin:5px"&gt;
                            &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
                          &lt;b&gt;&lt;h1&gt;AERO GATE TOPPER&lt;/h1&gt;&lt;/b&gt;
                        &lt;/div&gt;
                        &lt;div style="clear: both;"&gt;&lt;/div&gt;
                        
                        &lt;b&gt;  &lt;/b&gt;
                    &lt;/div&gt;
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                &lt;div style="clear: both;"&gt;&lt;/div&gt;

                &lt;div class="row" style="margin-top: 5px; display: flex;"&gt;                    
                    &lt;div class="col-md-8" id="question-container" style="width: 66.666666%;"&gt;
                        
                        &lt;!-- Question 1 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="A vector space is defined as a set of vectors closed under addition and scalar multiplication."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;1. Which of the following is a requirement for a set of vectors to form a vector space?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options1" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Vectors must have integer components&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options1" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The set must be closed under vector addition and scalar multiplication&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options1" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;All vectors must be orthogonal&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options1" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The set must contain only non-zero vectors&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 2 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The null space of a matrix consists of all vectors that satisfy A * x = 0, where A is the matrix and x is the vector."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;2. What does the null space of a matrix A represent?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The set of all vectors x such that A * x = 0&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The set of all vectors x such that A * x = x&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options2" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The set of all eigenvectors of A&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The set of all orthogonal vectors to A&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 3 (MSQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="MSQ" data-explanation="Eigenvalues are scalars that satisfy A * v = λ * v, where A is a square matrix, v is the eigenvector, and λ is the eigenvalue. Eigenvectors corresponding to different eigenvalues are linearly independent."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;3. Which of the following statements about eigenvalues and eigenvectors are true?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options3" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Eigenvalues are scalars that scale eigenvectors&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options3" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Eigenvectors corresponding to the same eigenvalue are always orthogonal&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options3" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Eigenvectors corresponding to different eigenvalues are linearly independent&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options3" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;The sum of two eigenvectors is always an eigenvector&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 4 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The characteristic equation of a matrix is obtained by solving det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;4. What equation must be satisfied for λ to be an eigenvalue of a matrix A?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options4" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;A * v = v&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options4" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;A * λ = v&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options4" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;det(A - λI) = 0&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options4" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;det(A - λA) = 1&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 5 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Linear Algebra" data-type="MCQ" data-explanation="For an orthogonal matrix, the transpose of the matrix is equal to its inverse, i.e., Aᵀ = A⁻¹."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;5. For an orthogonal matrix A, which of the following is true?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Aᵀ * A = A&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Aᵀ * A = I&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;A * Aᵀ = 0&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;A⁻¹ * A = A&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 6 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="The Gram-Schmidt process converts a set of linearly independent vectors into an orthonormal set. It is often used in QR decomposition."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;6. The Gram-Schmidt process is used to:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options6" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Solve systems of linear equations&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options6" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Calculate determinants of matrices&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options6" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Orthogonalize a set of vectors&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options6" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Diagonalize matrices&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 7 (MSQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="A;B" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="MSQ" data-explanation="The rank-nullity theorem states that for any matrix A, rank(A) + nullity(A) equals the number of columns of A."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;7. Which of the following statements about the rank-nullity theorem are true?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options7" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Rank(A) + Nullity(A) = Number of columns of A&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options7" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Rank(A) is the number of linearly independent rows or columns&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options7" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Nullity(A) is always greater than Rank(A)&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options7" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Rank(A) is equal to the dimension of the null space of A&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 8 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="For diagonalizable matrices, a matrix A can be expressed as A = PDP⁻¹, where D is a diagonal matrix of eigenvalues, and P is a matrix of eigenvectors."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;8. A matrix A is diagonalizable if:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;All of its eigenvalues are zero&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;It has a full set of linearly independent eigenvectors&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;It is a symmetric matrix&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It is invertible&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 9 (MCQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Linear Algebra" data-type="MCQ" data-explanation="A system of linear equations has a unique solution if the number of independent equations equals the number of unknowns, and the determinant of the coefficient matrix is non-zero."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;9. Under what conditions does a system of linear equations have a unique solution?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options9" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The determinant of the coefficient matrix is non-zero&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options9" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The number of equations is greater than the number of unknowns&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options9" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The matrix is symmetric&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options9" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The matrix has no eigenvalues&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 10 (MSQ - Theoretical) --&gt;
                        &lt;div class="question" data-answer="A;D" data-correct-score="2" data-incorrect-score="0" data-subject="Linear Algebra" data-type="MSQ" data-explanation="Orthogonal matrices have the property that their transpose is equal to their inverse. This makes them useful in various areas of numerical linear algebra."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;10. Which of the following statements about orthogonal matrices are true?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options10" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Aᵀ * A = I&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options10" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Orthogonal matrices are always diagonalizable&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options10" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;The determinant of an orthogonal matrix is zero&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options10" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Orthogonal matrices preserve vector lengths under transformations&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;










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            let currentSubject = '';
            let timerInterval; 
            const questionStartTimes = [];
            let timeTakenArray = {};
            let subjectData = {};
            let userName = '';
            let countdownMinutes = 45;
            let countdownSeconds = countdownMinutes * 60;
            let targetTime;
            document.getElementById("registrationForm").addEventListener("submit", function(e) {
              e.preventDefault();
              var formData = new FormData(this);
              userName = formData.get('username');

              // Hide user-info and show start-page immediately
              document.getElementById('user-info').style.display = 'none';
              document.getElementById('start-page').style.display = 'block';

              fetch("https://script.google.com/macros/s/AKfycbyrfDJmI2KwyzUJOY8yCTTpuHIuqSLu2gbGPC0q8Lvqd7GeURM9PjqtKjXXkG9E14dO/exec", {
                  method: "POST",
                  body: formData
              })
              .then(response =&gt; response.json())
              .then(data =&gt; {
                  if (!data.success) {
                      alert("Error: " + data.error);
                      // Optionally show the user-info back if there was an error
                      document.getElementById('user-info').style.display = 'block';
                      document.getElementById('start-page').style.display = 'none';
                  }
              })
              .catch(error =&gt; {
                  console.error("Fetch error:", error);
                  alert("There was an error processing your request.");
                  // Optionally show the user-info back if there was an error
                  document.getElementById('user-info').style.display = 'block';
                  document.getElementById('start-page').style.display = 'none';
              });
          });
            
            document.getElementById('calc-btn').addEventListener('click', function () {
                const calcContainer = document.getElementById('calc-container');
                if (calcContainer.style.display === 'none' || calcContainer.style.display === '') {
                    calcContainer.style.display = 'block';
                } else {
                    calcContainer.style.display = 'none';
                }
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.appendChild(calcContainer);
            });

            const calcContainer = document.getElementById('calc-container');
            let offsetX, offsetY, isDragging = false;
            calcContainer.style.position = 'absolute';

            calcContainer.addEventListener('mousedown', (e) =&gt; {
                isDragging = true;
                offsetX = e.clientX - calcContainer.getBoundingClientRect().left;
                offsetY = e.clientY - calcContainer.getBoundingClientRect().top;
                document.addEventListener('mousemove', moveAt);
            });

            document.addEventListener('mouseup', () =&gt; {
                if (isDragging) {
                    isDragging = false;
                    document.removeEventListener('mousemove', moveAt);
                }
            });

            function moveAt(e) {
                if (isDragging) {
                    const newLeft = e.clientX - offsetX;
                    const newTop = e.clientY - offsetY;
                    calcContainer.style.left = newLeft + 'px';
                    calcContainer.style.top = newTop + 'px';
                }
            }

            function initializeSubjectData() {
                const questionElements = document.querySelectorAll('.question');
                questionElements.forEach((question) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjectData[subject]) {
                        subjectData[subject] = {
                            markedForReview: new Set(),
                            answeredQuestions: new Set(),
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            totalQuestions: 0
                        };
                    }
                    timeTakenArray[subject] = [];
                    subjectData[subject].totalQuestions++;
                });
            }

            document.getElementById('start-button').onclick = function() {
                document.getElementById('start-page').style.display = 'none';
                document.getElementById('fullscreen-container').style.display = 'block';
                startQuiz();
            };

            function startQuiz() {
                initializeSubjectData();
                showSubject('Linear Algebra');
                questionStartTimes[currentQuestionIndex] = Date.now();
                startCountdown();
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                document.addEventListener('keydown', function(event) {
                    event.preventDefault();
                });
                document.addEventListener('contextmenu', function(e) {
                    e.preventDefault();
                });
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            }

            function showSubject(subject) {
                currentSubject = subject;
                questions = Array.from(document.querySelectorAll(`.question[data-subject="${subject}"]`));
                currentQuestionIndex = 0;
                updateQuestionDisplay();
                updateFooterButtons();
                updateQuestionPalette();
                questionStartTimes[currentQuestionIndex] = Date.now();
            }

            function updateQuestionDisplay() {
                document.querySelectorAll('.question').forEach((question) =&gt; {
                    question.style.display = 'none';
                });
                if (questions.length &gt; 0) {
                    questions[currentQuestionIndex].style.display = 'block';
                    if (questions[currentQuestionIndex].getAttribute('data-type') === 'NAT') {
                        document.getElementById('numeric-keypad').style.display = 'block';
                    } else {
                        document.getElementById('numeric-keypad').style.display = 'none';
                    }
                }
            }

            function updateFooterButtons() {
                document.getElementById('prev').style.display = currentQuestionIndex === 0 ? 'none' : 'inline';
                document.getElementById('next').style.display = currentQuestionIndex === questions.length - 1 ? 'none' : 'inline';
                document.getElementById('footer_buttons').style.display = questions.length &gt; 0 ? 'block' : 'none';
            }

            document.getElementById('prev').onclick = function(){
                if (currentQuestionIndex &gt; 0) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex--;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('next').onclick = function(){
                if (currentQuestionIndex &lt; questions.length - 1) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex++;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('clear').onclick = function(){
                const currentQuestion = questions[currentQuestionIndex];
                currentQuestion.querySelectorAll('input:checked').forEach(input =&gt; input.checked = false);
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                
                updateQuestionPalette();
            }

            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestionIndex];
                const timeTaken = (questionEndTime - questionStartTime) / 1000;
                const subject = currentSubject;            
                if (!timeTakenArray[subject]) {
                    timeTakenArray[subject] = {};
                }
                if (!timeTakenArray[subject][currentQuestionIndex]) {
                    timeTakenArray[subject][currentQuestionIndex] = 0;
                }
                timeTakenArray[subject][currentQuestionIndex] += timeTaken;
                questionStartTimes[currentQuestionIndex] = questionEndTime;
            }

            document.getElementById('submit').onclick = function(){
                recordTimeTaken();
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';    
                document.getElementById('confirmSubmit').onclick = function() {
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    modal.style.display = 'none';    
                    const adModal = document.getElementById('adModal');
                    const adCloseButton = document.getElementById('adClose');
                    adModal.style.display = 'block';    
                    setTimeout(() =&gt; {
                        adCloseButton.style.display = 'inline';
                    }, 5000);    
                    adCloseButton.onclick = function() {
                        adModal.style.display = 'none';
                        displayResults(); // Ensure this function is called to show results
                    };    
                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block'; // Show result container
                            showResult(); // Ensure this function is called to show results
                        }
                    }, 10000);    
                    clearInterval(timerInterval);
                };    
                document.getElementById('cancelSubmit').onclick = function() {
                    modal.style.display = 'none';
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                };    
                const exitFullScreen = document.exitFullscreen || document.mozCancelFullScreen || document.webkitExitFullscreen || document.msExitFullscreen;
                if (exitFullScreen) exitFullScreen.call(document);
            }

            function displayResults() {
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('user-name-display').innerText = userName;
                showResult();
                // window.location.href = './results.html'; 
            }

            document.getElementById('mark-for-review').onclick = function()  {
                const subjectMarks = subjectData[currentSubject].markedForReview;
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                if (subjectMarks.has(currentQuestionIndex)) {
                    subjectMarks.delete(currentQuestionIndex);
                } else {
                    subjectMarks.add(currentQuestionIndex);
                }
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }
                updateQuestionPalette();
            }

            function handleQuestionStateBeforeChange() {
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);

                // Save the user's answer
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }

                // Always mark the question as seen
                markAsSeen(currentQuestionIndex);
            }

            function updateQuestionStats() {
                // Count answered questions (green buttons)
                const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'green').length;

                // Count marked for review questions (orange buttons)
                const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'orange').length;

                // Total questions in the current subject
                const totalQuestions = questions.length;

                // Count unanswered questions (red buttons)
                const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'red').length;

                // Count not visited questions (black buttons)
                const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'black').length;

                // Update the counts in the HTML
                document.getElementById('answered-count').textContent = `${answeredCount}`;
                document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
                document.getElementById('review-count').textContent = `${markedForReviewCount}`;
                document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
            }

            function updateQuestionPalette() {
                const palette = document.getElementById('question-palette');
                palette.innerHTML = '';
                palette.appendChild(document.createElement('br'));
                palette.appendChild(document.createElement('hr'));
                const subjectHeading = document.createElement('h3');
                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            /* function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            } */

            function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;
            
                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;
            
                    // Convert time spent on the current subject to minutes and seconds
                    const subjectMinutes = Math.floor(subjectResult.timeSpent / 60);
                    const subjectSeconds = subjectResult.timeSpent % 60;
            
                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${subjectMinutes.toString().padStart(2, '0')}min:${subjectSeconds.toString().padStart(2, '0')}secs&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }
            
                // Convert totalTimeSpent (in seconds) to minutes and seconds
                const totalMinutes = Math.floor(totalTimeSpent / 60);
                const totalSeconds = totalTimeSpent % 60;
            
                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${totalMinutes.toString().padStart(2, '0')}min:${totalSeconds.toString().padStart(2, '0')}secs&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            }
            
            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/linear-algebra-1.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-8372617494647323903</guid><pubDate>Mon, 28 Oct 2024 12:43:00 +0000</pubDate><atom:updated>2025-03-23T15:14:38.447+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Thermal Stress &amp; Strain</title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Thermal Stress &amp; Strain Topic-wise Online Quiz&lt;/title&gt;
      &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
        &lt;!-- &lt;link href="quiz.css" rel="stylesheet"&gt; --&gt;
        &lt;meta charset="UTF-8"&gt;&lt;/meta&gt;
        &lt;meta content="width=device-width, initial-scale=1.0" name="viewport"&gt;&lt;/meta&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        
        &lt;style&gt;
          .col-lg-3{
            display:none;
          }
          .col-lg-9{
            flex: 0 0 100%;
          }
            .container{
	            padding:5px;
            }

            img{
            
            border:0px;
            }
            /* .options{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            } */
            .options div{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            }

            #question-container{
            
                padding:4px;
                height:35%;
                overflow-y:auto;
                padding-bottom: 100px;
                
            }
            
            #footer_buttons{
                display: none;
                position:fixed;
                bottom:0px;
                background:#ffffff;
                width:100%;
                height:80px;
                padding:4px;		
                border-top:1px solid #dddddd;
            }
            /* .question-info{
                margin: 5px auto;
                padding: 5px 0px 20px;
                border-bottom: 1px solid #CECECE;
                overflow-y: auto;
            } */
            #fullscreen-container row{
                margin-right: -15px;
                margin-left: -15px;
                display: flex;
                gap:15px;
                width: 100%;
            }
            #fullscreen-container row col-md-8, col-md-4{
                position: relative;
                min-height: 1px;
                padding-left: 15px;
                padding-right: 15px;
            }
            #fullscreen-container row col-md-8{
                float:left;
                width: 66.66666667%;
            }
            #fullscreen-container  row col-md-4{
                float:right;
                width: 33.33333333%;
            }
            .container-fluid{
                padding-left: 15px;
                padding-right: 15px;
                margin-left: auto;
                margin-right: auto;
            }
            #fullscreen-container{
                display: none;
                background-color: #ffffff;
                overflow: auto;
            }
            .quiz-attempt-inline-block{
                display: inline-block;
                width: 180px;
            }
         	#fullscreen-container .question-palette button {
              width: 40px;
              margin: 5px;
              padding: 5px;
            }
            @media(max-width:900px){
               #fullscreen-container button #confirmSubmit #cancelSubmit #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                gap:10px;
                font-size: 12px;
            }
                #fullscreen-container .row .col-md-4 .col-md-8 .options{
                    font-size: 12px;
                }
                #fullscreen-container .col-md-4{
                    width: 33.33333333%;
                }
                #fullscreen-container .col-md-8{
                    width: 66.66666667%;
                }
                 #fullscreen-container #footer_buttons{
                    bottom:0px;
                  	height:auto;
                }

                #fullscreen-container.quiz-attempt-inline-block{
                    display: flex;
                }
                #answered-count, #unanswered-count,#review-count,#not-visited-count {
                    width:20px;
                    margin: 5px;
                    padding: 5px;
                }
                #fullscreen-container h1 p{
                    font-size: 12px;
                }
              
                #fullscreen-container .question-palette h3{
                  font-size:14px;
                  font-weight:bold;
                }
                #calc-container {
                  position: absolute;
                  top: 30%;
                  left: 50%;
              	}
            }

            .angled-text {
                text-align: center;
                transform: rotate(-45deg);
                font-size: 44px;
                font-weight: bolder;
                color: rgba(19, 17, 17, 0.352);
                z-index: 1;
            }




        &lt;/style&gt;

        &lt;style&gt;
            body {
                font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
                margin: 0;
                padding: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #333;
                background-color: #f2f2f2;
            }

            /* #cont, #quiz-container, #container {
                background-color: #fff;
            }

            #cont {
                overflow: auto;
                height: 100vh;
                flex-wrap: wrap;
                flex-direction: row;
            } */
/* 
            .question {
                margin-top: 10px;
                padding: 10px;
                overflow-y: auto;
                display: none;
                width: 70%;
                margin-bottom: 20px;
            } */

            h1, p {
                font-size: 16px;
                margin-top: 20px;
                color: #333;
            }

            .options {
                display: flex;
                flex-direction: column;
                flex-wrap: wrap;
                gap: 10px;
            }

            .options div {
                display: flex;
                align-items: center;
            }

            label {
                margin-left: 5px;
                font-size: 14px;
                color: #333;
            }

            input[type="radio"], input[type="checkbox"] {
                padding: 8px;
                margin-bottom: 10px;
                border: 1px solid #ccc;
                border-radius: 3px;
            }

            input[type="radio"]:focus, input[type="checkbox"]:focus {
                outline: none;
                border-color: #007bff;
            }

            button, #confirmSubmit, #cancelSubmit, #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                margin-left: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #fff;
                border: none;
                background-color: #0056b3;
                border-radius: 4px;
                cursor: pointer;
                transition: background-color 0.3s ease;
            }

            button:hover, #submit-user-info:hover {
                background-color: #0056b3;
            }

            #confirmSubmit {
                background-color: #5bc0de;
            }

            #confirmSubmit:hover {
                background-color: #3fb5da;
            }

            #cancelSubmit {
                background-color: #d9534f;
            }

            #cancelSubmit:hover {
                background-color: #d43f3a;
            }

            #clear, #prev, #next, #mark-for-review, #submit {
                padding: 10px 20px;
                border-radius: 4px;
                cursor: pointer;
            }

            #prev, #next {
                background-color: #5cb85c;
            }

            #prev:hover, #next:hover {
                background-color: #4cae4c;
            }

            #mark-for-review {
                background-color: #f0ad4e;
            }

            #submit {
                background-color: #d9534f;
            }

            #submit:hover {
                background-color: #d43f3a;
            }

            /* #result {
                text-align: center;
                font-size: 20px;
                font-weight: bold;
                margin-top: 20px;
            }

            #score-summary {
                width: 95%;
                border-collapse: collapse;
                margin-top: 20px;
                margin-bottom: 20px;
            }

            #score-summary th, #score-summary td {
                padding: 10px;
                text-align: center;
            }

            #score-summary tbody tr:nth-child(odd) {
                background-color: #f9f9f9;
            }

            #score-summary tbody tr:hover {
                background-color: #e0e0e0;
            } */

            #user-info {
                max-width: 400px;
                margin: 0 auto;
                padding: 20px;
                background-color: #f9f9f9;
                border-radius: 8px;
                box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
                text-align: center;
            }

            #user-info input[type="text"], #user-info input[type="email"] {
                width: 90%;
                padding: 10px;
                margin-bottom: 15px;
                border: 2px solid #ccc;
                border-radius: 4px;
                font-size: 16px;
            }

            #user-info input[type="text"]:focus, #user-info input[type="email"]:focus {
                border-color: #007bff;
                box-shadow: 0 0 5px rgba(0, 123, 255, 0.5);
            }

            .question-palette {
                background-color: #fff;
            }

            .question-palette button {
                margin: 10px;
                padding: 10px;
                border: 1px solid #ccc;
                background-color: black;
                color: white;
            }

            .correct-answer {
                background-color: #71ba5d;
                color: white;
            }

            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
            }

            .not-answered {
                background-color: #fff;
                color: black;
            }

            table {
                width: 100%;
                border-collapse: collapse;
                margin-bottom: 20px;
            }

            th, td {
                border: 1px solid #ddd;
                padding: 8px;
            }

            th {
                background-color: #f2f2f2;
                text-align: left;
                font-weight: bold;
            }

            .category-row {
                background-color: #e0f7fa; /* Light cyan */
            }

            .total-row {
                background-color: #ffe0b2; /* Light orange */
            }

            .modal, .admodal {
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
                top: 0;
                width: 100%;
                height: 100%;
                background-color: rgba(0, 0, 0, 0.4);
            }

            .modal-content, .admodal-content {
                background-color: white;
                margin: 15% auto;
                padding: 20px;
                border: 1px solid #888;
                width: 80%;
                max-width: 400px;
                text-align: center;
                border-radius: 5px;
            }

            .adclose {
                color: #aaa;
                float: right;
                font-size: 28px;
                font-weight: bold;
            }

            .adclose:hover, .adclose:focus {
                color: black;
                cursor: pointer;
            }

            #start-page {
                display: none;
                padding: 20px;
                background-color: #fff;
            }

            #start-button {
                display: inline-block;
                padding: 10px;
                font-size: 18px;
                background-color: #007bff;
                color: #fff;
            }
              #numeric-keypad {                
                margin-top:50px;
                background-color: #f9f9f9;
                box-shadow: 0 -2px 10px rgba(0, 0, 0, 0.2);
                padding: 10px; 
                z-index: 1000;
              }

              #numeric-keypad .options {
                  display: flex;
                  flex-direction: column;
                  align-items: center;
              }

              #numeric-keypad h3 {
                  margin: 0 0 10px; 
              }

              #numeric-keypad div {
                  display: flex;
                  justify-content: center;
                  margin-bottom: 5px;
              }

              #numeric-keypad button {
                  background-color: #4185f2;
                width:30px;
                  color: white;
                  border: none;
                  border-radius: 5px;
                  padding: 10px;
                  font-size: 15px;
                  margin: 0 5px;
                  cursor: pointer;
                  transition: background-color 0.3s;
              }

              #numeric-keypad button:hover {
                  background-color: #0056b3;
              }

              #numeric-keypad button:active {
                  background-color: #004080;
              }

            @media screen and (max-width: 900px) {
                body, p, label {
                    font-size: 14px;
                }

                .question-palette button {
                    text-align: center;
                }
            }
            .question-info {
                display: flex;
                flex-direction: column;
                gap: 10px; /* Adjust the spacing between elements */
            }

            #calc-container {
                  position: absolute;
                  top: 30%;
                  margin-left: 50%;
            }
            #detailed-results .question-result{
              padding:30px;
              border: 2px solid black;
            }
            #detailed-results{
              left: 20px; 
              padding:20px;
            }
            #detailed-results h3{
            text-align:center; 
            font-size:25px; 
            font-weight:bold;
            }
        &lt;/style&gt;
    &lt;/head&gt;
    &lt;body&gt;
        &lt;div id="user-info"&gt;
          &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;form id="registrationForm"&gt;            
                &lt;h1&gt;Enter Your Details&lt;/h1&gt;
               	&lt;input type="hidden" id="password" name="password" value="Thermal Stress &amp; Strain" /&gt;
                &lt;label for="name"&gt;Name:&lt;/label&gt;
                &lt;input id="username" name="username" required="" type="text" /&gt;
                &lt;!-- &lt;label for="email"&gt;Email:&lt;/label&gt;
                &lt;input id="email" name="email" required="" type="email" /&gt; --&gt;
                &lt;button type="submit" id="submit-user-info"&gt;Next&lt;/button&gt;
            &lt;/form&gt;
             &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
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                        &lt;!-- Question 1 (Numerical) --&gt;
                        &lt;div class="question" data-answer="30" data-correct-score="1" data-incorrect-score="0" data-max="32" data-min="28" data-precision="0" data-subject="Thermal Stress and Strain" data-type="NAT" data-explanation="Thermal stress, σ = α * E * ΔT, where α is the coefficient of thermal expansion, E is the modulus of elasticity, and ΔT is the temperature change."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;1. A steel bar is fixed at both ends and experiences a temperature rise of 50°C. The coefficient of thermal expansion is 12 × 10⁻⁶ /°C and the modulus of elasticity is 200 GPa. Calculate the thermal stress developed in the bar (in MPa). Use whole numbers only.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer1" name="nat-options" type="text" /&gt;
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                        &lt;!-- Question 2 (MCQ) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Thermal Stress and Strain" data-type="MCQ" data-explanation="When temperature changes, the material tries to expand or contract, and if constrained, it results in thermal stress. These stresses are compressive when temperature decreases and tensile when temperature increases."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;2. What happens to the thermal stress in a material if it is heated while being completely constrained?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The material experiences compressive stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The material expands freely&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options2" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The material experiences tensile stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The stress does not change&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 3 (MSQ) --&gt;
                        &lt;div class="question" data-answer="A;D" data-correct-score="2" data-incorrect-score="0" data-subject="Thermal Stress and Strain" data-type="MSQ" data-explanation="When materials are subjected to thermal stress, factors like temperature change and modulus of elasticity determine the induced stresses. Thermal expansion also depends on the material's coefficient of thermal expansion."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;3. Which factors influence the thermal stress developed in a constrained material?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options3" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Temperature change&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options3" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Applied force&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options3" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Cross-sectional area&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options3" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Coefficient of thermal expansion&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 4 (Numerical) --&gt;
                        &lt;div class="question" data-answer="0.0012" data-correct-score="2" data-incorrect-score="0" data-max="0.0015" data-min="0.001" data-precision="4" data-subject="Thermal Stress and Strain" data-type="NAT" data-explanation="Thermal strain, ε = α * ΔT, where α is the coefficient of thermal expansion and ΔT is the temperature change."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;4. A metal rod with a coefficient of thermal expansion of 12 × 10⁻⁶ /°C experiences a temperature increase of 100°C. Calculate the thermal strain. Use four decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer4" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 5 (MCQ) --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Thermal Stress and Strain" data-type="MCQ" data-explanation="In a constrained bar, thermal stress develops due to the restraint on free expansion or contraction, leading to compressive stress when cooled."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;5. A steel bar is constrained at both ends and experiences a temperature drop. Which type of stress is generated in the bar?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Compressive stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Tensile stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Shear stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;No stress&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 6 (MSQ) --&gt;
                        &lt;div class="question" data-answer="A;B" data-correct-score="2" data-incorrect-score="0" data-subject="Thermal Stress and Strain" data-type="MSQ" data-explanation="Both Young’s modulus and the coefficient of thermal expansion contribute to thermal stresses in a constrained material as they control how much strain results from temperature changes."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;6. Which material properties influence the amount of thermal stress generated in a constrained structure?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options6" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Young’s modulus&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options6" type="&lt;!-- Question 6 (continued) --&gt;
                                checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Coefficient of thermal expansion&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options6" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Density of material&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options6" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Poisson’s ratio&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 7 (Numerical) --&gt;
                        &lt;div class="question" data-answer="45" data-correct-score="2" data-incorrect-score="0" data-max="48" data-min="42" data-precision="0" data-subject="Thermal Stress and Strain" data-type="NAT" data-explanation="Thermal stress, σ = α * E * ΔT. The temperature drop leads to compressive stress in a material when constrained."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;7. A copper bar with a coefficient of thermal expansion of 16 × 10⁻⁶ /°C is constrained at both ends and undergoes a temperature drop of 30°C. If the modulus of elasticity is 120 GPa, calculate the compressive thermal stress generated in the bar (in MPa). Use whole numbers only.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer7" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 8 (MCQ) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Thermal Stress and Strain" data-type="MCQ" data-explanation="In the absence of constraints, a material is free to expand or contract without generating any internal stress. Constraints cause stress to develop."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;8. What will happen to the thermal stress in a material if it is free to expand or contract during temperature changes?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;It will experience tensile stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;No stress will develop&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;It will experience compressive stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;It will experience both tensile and compressive stress&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 9 (MSQ) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="0" data-subject="Thermal Stress and Strain" data-type="MSQ" data-explanation="The total strain is the combination of mechanical and thermal strains in a constrained material, and the thermal stress depends on the modulus of elasticity and coefficient of thermal expansion."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;9. Which of the following factors contribute to the combined strain in a material subjected to both mechanical and thermal loading?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options9" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Applied mechanical load&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options9" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Material density&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options9" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Temperature change&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options9" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Poisson’s ratio&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 10 (Numerical) --&gt;
                        &lt;div class="question" data-answer="10" data-correct-score="2" data-incorrect-score="0" data-max="12" data-min="8" data-precision="0" data-subject="Thermal Stress and Strain" data-type="NAT" data-explanation="ΔL = L * α * ΔT, where L is the original length, α is the coefficient of thermal expansion, and ΔT is the temperature change."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;10. A steel rod of length 2 meters is subjected to a temperature increase of 50°C. The coefficient of thermal expansion for steel is 12 × 10⁻⁶ /°C. Calculate the change in length (in mm). Use whole numbers only.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer10" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 11 (MCQ) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Thermal Stress and Strain" data-type="MCQ" data-explanation="Thermal stress occurs due to the material being constrained from free expansion or contraction when there is a temperature change."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;11. Which of the following is a consequence of thermal stress in a constrained material?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options11" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Reduction in modulus of elasticity&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options11" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Free expansion of the material&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options11" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Internal stresses due to temperature change&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options11" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Material remains stress-free&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 12 (MSQ) --&gt;
                        &lt;div class="question" data-answer="B;D" data-correct-score="1" data-incorrect-score="0" data-subject="Thermal Stress and Strain" data-type="MSQ" data-explanation="The modulus of elasticity and coefficient of thermal expansion directly influence how much strain and stress develop when a material is constrained under thermal loading."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;12. Which factors affect the thermal strain in a material subjected to temperature change?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options12" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Material density&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options12" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Coefficient of thermal expansion&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options12" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Thermal conductivity&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options12" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Modulus of elasticity&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 13 (MCQ - Direct Relation) --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Stress and Strain" data-type="MCQ" data-explanation="According to Hooke’s Law, σ = E * ε, where σ is stress, E is Young’s modulus, and ε is strain."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
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                            &lt;/div&gt;
                            &lt;p&gt;13. What is the direct relationship between stress (σ) and strain (ε) in the elastic region of a material?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options13" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;σ = E * ε&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options13" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;σ = ε / E&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options13" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;σ = E / ε&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options13" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;σ = ε² / E&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 14 (MSQ - Direct Relation) --&gt;
                        &lt;div class="question" data-answer="A;B" data-correct-score="1" data-incorrect-score="0" data-subject="Stress and Strain" data-type="MSQ" data-explanation="The strain energy in a material is related to the applied stress and strain as U = (σ² / 2E) or U = (1/2) * σ * ε for a linear elastic material."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;14. Which of the following are correct expressions for strain energy (U) in a material subjected to stress (σ) and strain (ε)?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options14" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;U = (σ² / 2E)&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options14" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;U = (1/2) * σ * ε&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options14" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;U = σ * ε / 3&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options14" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;U = 2 * σ * ε&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 15 (MCQ - Direct Relation) --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Thermal Stress and Strain" data-type="MCQ" data-explanation="The thermal strain (ε) is directly proportional to the temperature change, ΔT, as ε = α * ΔT, where α is the coefficient of thermal expansion."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;15. How is thermal strain (ε) related to the temperature change (ΔT) and coefficient of thermal expansion (α)?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;ε = ΔT / α&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options15" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;ε = α / ΔT&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;ε = ΔT² * α&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;ε = α * ΔT&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 16 (MSQ - Direct Relation) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="1" data-incorrect-score="0" data-subject="Stress and Strain" data-type="MSQ" data-explanation="Hooke’s Law and thermal strain relations both involve Young’s modulus (E) and the coefficient of thermal expansion (α), affecting stress and strain."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;16. Which of the following relations involve Young’s modulus (E) and the coefficient of thermal expansion (α)?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options16" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;σ = E * ε&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options16" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;ε = σ / α&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options16" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;σ = α * E * ΔT&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options16" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;σ = ΔT / α * E&lt;/label&gt;&lt;/div&gt;
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                    e.preventDefault();
                });
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            }

            function showSubject(subject) {
                currentSubject = subject;
                questions = Array.from(document.querySelectorAll(`.question[data-subject="${subject}"]`));
                currentQuestionIndex = 0;
                updateQuestionDisplay();
                updateFooterButtons();
                updateQuestionPalette();
                questionStartTimes[currentQuestionIndex] = Date.now();
            }

            function updateQuestionDisplay() {
                document.querySelectorAll('.question').forEach((question) =&gt; {
                    question.style.display = 'none';
                });
                if (questions.length &gt; 0) {
                    questions[currentQuestionIndex].style.display = 'block';
                    if (questions[currentQuestionIndex].getAttribute('data-type') === 'NAT') {
                        document.getElementById('numeric-keypad').style.display = 'block';
                    } else {
                        document.getElementById('numeric-keypad').style.display = 'none';
                    }
                }
            }

            function updateFooterButtons() {
                document.getElementById('prev').style.display = currentQuestionIndex === 0 ? 'none' : 'inline';
                document.getElementById('next').style.display = currentQuestionIndex === questions.length - 1 ? 'none' : 'inline';
                document.getElementById('footer_buttons').style.display = questions.length &gt; 0 ? 'block' : 'none';
            }

            document.getElementById('prev').onclick = function(){
                if (currentQuestionIndex &gt; 0) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex--;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('next').onclick = function(){
                if (currentQuestionIndex &lt; questions.length - 1) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex++;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('clear').onclick = function(){
                const currentQuestion = questions[currentQuestionIndex];
                currentQuestion.querySelectorAll('input:checked').forEach(input =&gt; input.checked = false);
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                
                updateQuestionPalette();
            }

            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestionIndex];
                const timeTaken = (questionEndTime - questionStartTime) / 1000;
                const subject = currentSubject;            
                if (!timeTakenArray[subject]) {
                    timeTakenArray[subject] = {};
                }
                if (!timeTakenArray[subject][currentQuestionIndex]) {
                    timeTakenArray[subject][currentQuestionIndex] = 0;
                }
                timeTakenArray[subject][currentQuestionIndex] += timeTaken;
                questionStartTimes[currentQuestionIndex] = questionEndTime;
            }

            document.getElementById('submit').onclick = function(){
                recordTimeTaken();
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';    
                document.getElementById('confirmSubmit').onclick = function() {
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    modal.style.display = 'none';    
                    const adModal = document.getElementById('adModal');
                    const adCloseButton = document.getElementById('adClose');
                    adModal.style.display = 'block';    
                    setTimeout(() =&gt; {
                        adCloseButton.style.display = 'inline';
                    }, 5000);    
                    adCloseButton.onclick = function() {
                        adModal.style.display = 'none';
                        displayResults(); // Ensure this function is called to show results
                    };    
                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block'; // Show result container
                            showResult(); // Ensure this function is called to show results
                        }
                    }, 10000);    
                    clearInterval(timerInterval);
                };    
                document.getElementById('cancelSubmit').onclick = function() {
                    modal.style.display = 'none';
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                };    
                const exitFullScreen = document.exitFullscreen || document.mozCancelFullScreen || document.webkitExitFullscreen || document.msExitFullscreen;
                if (exitFullScreen) exitFullScreen.call(document);
            }

            function displayResults() {
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('user-name-display').innerText = userName;
                showResult();
                // window.location.href = './results.html'; 
            }

            document.getElementById('mark-for-review').onclick = function()  {
                const subjectMarks = subjectData[currentSubject].markedForReview;
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                if (subjectMarks.has(currentQuestionIndex)) {
                    subjectMarks.delete(currentQuestionIndex);
                } else {
                    subjectMarks.add(currentQuestionIndex);
                }
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }
                updateQuestionPalette();
            }

            function handleQuestionStateBeforeChange() {
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);

                // Save the user's answer
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }

                // Always mark the question as seen
                markAsSeen(currentQuestionIndex);
            }

            function updateQuestionStats() {
                // Count answered questions (green buttons)
                const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'green').length;

                // Count marked for review questions (orange buttons)
                const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'orange').length;

                // Total questions in the current subject
                const totalQuestions = questions.length;

                // Count unanswered questions (red buttons)
                const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'red').length;

                // Count not visited questions (black buttons)
                const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'black').length;

                // Update the counts in the HTML
                document.getElementById('answered-count').textContent = `${answeredCount}`;
                document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
                document.getElementById('review-count').textContent = `${markedForReviewCount}`;
                document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
            }

            function updateQuestionPalette() {
                const palette = document.getElementById('question-palette');
                palette.innerHTML = '';
                palette.appendChild(document.createElement('br'));
                palette.appendChild(document.createElement('hr'));
                const subjectHeading = document.createElement('h3');
                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            }

            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/thermal-stress-strain.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-6156731263875952110</guid><pubDate>Sun, 27 Oct 2024 17:12:00 +0000</pubDate><atom:updated>2025-03-23T15:15:19.857+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Stress &amp; Strain</title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Stress &amp; Strain Topic-wise Online Quiz&lt;/title&gt;
      &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
      
        &lt;!-- &lt;link href="quiz.css" rel="stylesheet"&gt; --&gt;
        &lt;meta charset="UTF-8"&gt;&lt;/meta&gt;
        &lt;meta content="width=device-width, initial-scale=1.0" name="viewport"&gt;&lt;/meta&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        
        &lt;style&gt;
          .col-lg-3{
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            .container{
	            padding:5px;
            }

            img{
            
            border:0px;
            }
            /* .options{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            } */
            .options div{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            }

            #question-container{
            
                padding:4px;
                height:35%;
                overflow-y:auto;
                padding-bottom: 100px;
                
            }
            
            #footer_buttons{
                display: none;
                position:fixed;
                bottom:0px;
                background:#ffffff;
                width:100%;
                height:80px;
                padding:4px;		
                border-top:1px solid #dddddd;
            }
            /* .question-info{
                margin: 5px auto;
                padding: 5px 0px 20px;
                border-bottom: 1px solid #CECECE;
                overflow-y: auto;
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            #fullscreen-container row{
                margin-right: -15px;
                margin-left: -15px;
                display: flex;
                gap:15px;
                width: 100%;
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            #fullscreen-container row col-md-8, col-md-4{
                position: relative;
                min-height: 1px;
                padding-left: 15px;
                padding-right: 15px;
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            #fullscreen-container row col-md-8{
                float:left;
                width: 66.66666667%;
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            #fullscreen-container  row col-md-4{
                float:right;
                width: 33.33333333%;
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            .container-fluid{
                padding-left: 15px;
                padding-right: 15px;
                margin-left: auto;
                margin-right: auto;
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            #fullscreen-container{
                display: none;
                background-color: #ffffff;
                overflow: auto;
            }
            .quiz-attempt-inline-block{
                display: inline-block;
                width: 180px;
            }
         	#fullscreen-container .question-palette button {
              width: 40px;
              margin: 5px;
              padding: 5px;
            }
            @media(max-width:900px){
               #fullscreen-container button #confirmSubmit #cancelSubmit #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                gap:10px;
                font-size: 12px;
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                #fullscreen-container .row .col-md-4 .col-md-8 .options{
                    font-size: 12px;
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                #fullscreen-container .col-md-4{
                    width: 33.33333333%;
                }
                #fullscreen-container .col-md-8{
                    width: 66.66666667%;
                }
                 #fullscreen-container #footer_buttons{
                    bottom:0px;
                  	height:auto;
                }

                #fullscreen-container.quiz-attempt-inline-block{
                    display: flex;
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                #answered-count, #unanswered-count,#review-count,#not-visited-count {
                    width:20px;
                    margin: 5px;
                    padding: 5px;
                }
                #fullscreen-container h1 p{
                    font-size: 12px;
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                #fullscreen-container .question-palette h3{
                  font-size:14px;
                  font-weight:bold;
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                  position: absolute;
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                  left: 50%;
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                transform: rotate(-45deg);
                font-size: 44px;
                font-weight: bolder;
                color: rgba(19, 17, 17, 0.352);
                z-index: 1;
            }




        &lt;/style&gt;

        &lt;style&gt;
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            #cont {
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                flex-direction: row;
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/* 
            .question {
                margin-top: 10px;
                padding: 10px;
                overflow-y: auto;
                display: none;
                width: 70%;
                margin-bottom: 20px;
            } */

            h1, p {
                font-size: 16px;
                margin-top: 20px;
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            .options {
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                flex-direction: column;
                flex-wrap: wrap;
                gap: 10px;
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            .options div {
                display: flex;
                align-items: center;
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            label {
                margin-left: 5px;
                font-size: 14px;
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                margin-bottom: 10px;
                border: 1px solid #ccc;
                border-radius: 3px;
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                border-color: #007bff;
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                display: inline-block;
                padding: 6px 12px;
                margin-left: 0;
                font-size: 14px;
                line-height: 1.42857143;
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                border-radius: 4px;
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                transition: background-color 0.3s ease;
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            button:hover, #submit-user-info:hover {
                background-color: #0056b3;
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            #confirmSubmit {
                background-color: #5bc0de;
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            #confirmSubmit:hover {
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            #cancelSubmit {
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            #cancelSubmit:hover {
                background-color: #d43f3a;
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            #clear, #prev, #next, #mark-for-review, #submit {
                padding: 10px 20px;
                border-radius: 4px;
                cursor: pointer;
            }

            #prev, #next {
                background-color: #5cb85c;
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            #prev:hover, #next:hover {
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            #mark-for-review {
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                font-size: 20px;
                font-weight: bold;
                margin-top: 20px;
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            #score-summary {
                width: 95%;
                border-collapse: collapse;
                margin-top: 20px;
                margin-bottom: 20px;
            }

            #score-summary th, #score-summary td {
                padding: 10px;
                text-align: center;
            }

            #score-summary tbody tr:nth-child(odd) {
                background-color: #f9f9f9;
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            #score-summary tbody tr:hover {
                background-color: #e0e0e0;
            } */

            #user-info {
                max-width: 400px;
                margin: 0 auto;
                padding: 20px;
                background-color: #f9f9f9;
                border-radius: 8px;
                box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
                text-align: center;
            }

            #user-info input[type="text"], #user-info input[type="email"] {
                width: 90%;
                padding: 10px;
                margin-bottom: 15px;
                border: 2px solid #ccc;
                border-radius: 4px;
                font-size: 16px;
            }

            #user-info input[type="text"]:focus, #user-info input[type="email"]:focus {
                border-color: #007bff;
                box-shadow: 0 0 5px rgba(0, 123, 255, 0.5);
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            .question-palette {
                background-color: #fff;
            }

            .question-palette button {
                margin: 10px;
                padding: 10px;
                border: 1px solid #ccc;
                background-color: black;
                color: white;
            }

            .correct-answer {
                background-color: #71ba5d;
                color: white;
            }

            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
            }

            .not-answered {
                background-color: #fff;
                color: black;
            }

            table {
                width: 100%;
                border-collapse: collapse;
                margin-bottom: 20px;
            }

            th, td {
                border: 1px solid #ddd;
                padding: 8px;
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            th {
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                text-align: left;
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            }

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            .total-row {
                background-color: #ffe0b2; /* Light orange */
            }

            .modal, .admodal {
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
                top: 0;
                width: 100%;
                height: 100%;
                background-color: rgba(0, 0, 0, 0.4);
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            .modal-content, .admodal-content {
                background-color: white;
                margin: 15% auto;
                padding: 20px;
                border: 1px solid #888;
                width: 80%;
                max-width: 400px;
                text-align: center;
                border-radius: 5px;
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            .adclose {
                color: #aaa;
                float: right;
                font-size: 28px;
                font-weight: bold;
            }

            .adclose:hover, .adclose:focus {
                color: black;
                cursor: pointer;
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            #start-page {
                display: none;
                padding: 20px;
                background-color: #fff;
            }

            #start-button {
                display: inline-block;
                padding: 10px;
                font-size: 18px;
                background-color: #007bff;
                color: #fff;
            }
              #numeric-keypad {                
                margin-top:50px;
                background-color: #f9f9f9;
                box-shadow: 0 -2px 10px rgba(0, 0, 0, 0.2);
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                z-index: 1000;
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              #numeric-keypad .options {
                  display: flex;
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              #numeric-keypad h3 {
                  margin: 0 0 10px; 
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              #numeric-keypad div {
                  display: flex;
                  justify-content: center;
                  margin-bottom: 5px;
              }

              #numeric-keypad button {
                  background-color: #4185f2;
                width:30px;
                  color: white;
                  border: none;
                  border-radius: 5px;
                  padding: 10px;
                  font-size: 15px;
                  margin: 0 5px;
                  cursor: pointer;
                  transition: background-color 0.3s;
              }

              #numeric-keypad button:hover {
                  background-color: #0056b3;
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              #numeric-keypad button:active {
                  background-color: #004080;
              }

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                body, p, label {
                    font-size: 14px;
                }

                .question-palette button {
                    text-align: center;
                }
            }
            .question-info {
                display: flex;
                flex-direction: column;
                gap: 10px; /* Adjust the spacing between elements */
            }

            #calc-container {
                  position: absolute;
                  top: 30%;
                  margin-left: 50%;
            }
            #detailed-results .question-result{
              padding:30px;
              border: 2px solid black;
            }
            #detailed-results{
              left: 20px; 
              padding:20px;
            }
            #detailed-results h3{
            text-align:center; 
            font-size:25px; 
            font-weight:bold;
            }
        &lt;/style&gt;
    &lt;/head&gt;
    &lt;body&gt;
        &lt;div id="user-info"&gt;
          &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;form id="registrationForm"&gt;            
                &lt;h1&gt;Enter Your Details&lt;/h1&gt;
               	&lt;input type="hidden" id="password" name="password" value="Stress &amp; Strain" /&gt;
                &lt;label for="name"&gt;Name:&lt;/label&gt;
                &lt;input id="username" name="username" required="" type="text" /&gt;
                &lt;!-- &lt;label for="email"&gt;Email:&lt;/label&gt;
                &lt;input id="email" name="email" required="" type="email" /&gt; --&gt;
                &lt;button type="submit" id="submit-user-info"&gt;Next&lt;/button&gt;
            &lt;/form&gt;
             &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
        &lt;/div&gt;
      
        &lt;div id="start-page" style="display: none;"&gt;
          &lt;center&gt;&lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;&lt;/center&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
            &lt;p&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;
                &lt;li&gt;The total duration of the examination is 45 minutes .&lt;/li&gt;
                &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
                &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
            &lt;/ol&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;To answer a question, do the following:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;&lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;&lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;&lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;               
            &lt;li&gt;
            You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;&lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To select your answer, click on the button on one of the options&lt;/li&gt;&lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;&lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next &lt;/b&gt;button&lt;/li&gt;&lt;/ol&gt;&lt;li&gt;
            Procedure for answering a numerical answer type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;&lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;&lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;&lt;/ol&gt;  
            &lt;li&gt;
            To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;&lt;/ol&gt;&lt;ol style="text-align: left;"&gt;
            &lt;/ol&gt;
            &lt;center&gt;&lt;button id="start-button"&gt;Start Quiz&lt;/button&gt;&lt;/center&gt;
        &lt;/div&gt;

        &lt;div class="modal" id="myModal" style="display: none;"&gt;
            &lt;div class="modal-content"&gt;
                &lt;h2&gt;Quiz Submission Confirmation&lt;/h2&gt;
                &lt;p&gt;Do you really want to submit this quiz?&lt;/p&gt;
                &lt;button id="confirmSubmit"&gt;Submit Quiz&lt;/button&gt;
                &lt;button id="cancelSubmit"&gt;Cancel&lt;/button&gt;
            &lt;/div&gt;
        &lt;/div&gt;

        &lt;div class="admodal" id="adModal" style="display: none;"&gt;
            &lt;div class="admodal-content"&gt;
                &lt;h2&gt;Advertisement&lt;/h2&gt;
                &lt;p&gt;Your Google Ad will be displayed here for 5 seconds.&lt;/p&gt;
                &lt;span class="adclose" id="adClose" style="display: none;"&gt;×&lt;/span&gt;
                &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
                &lt;ins class="adsbygoogle"
                    style="display:block; text-align:center;"
                    data-ad-layout="in-article"
                    data-ad-format="fluid"
                    data-ad-client="ca-pub-2922315402866630"
                    data-ad-slot="4993484640"&gt;&lt;/ins&gt;
                &lt;script&gt;
                    (adsbygoogle = window.adsbygoogle || []).push({});
                &lt;/script&gt;
            &lt;/div&gt;
        &lt;/div&gt;
        
        &lt;div id="fullscreen-container" style="display: none;"&gt;
            &lt;div class="container-fluid"&gt;
                &lt;div class="row" id="container" style="display: flex;"&gt;
                    &lt;div class="col-md-8" id="quiz-container" style="width: 66.666666%;"&gt;                        
                        &lt;div class="category-calculator"&gt;
                            &lt;div class="quiz-attempt-title" style="float: left; width: 33.333333%;"&gt;
                                &lt;p&gt;GATE Aerospace Basic Aerodyanamics&lt;/p&gt;
                            &lt;/div&gt;
                            &lt;div class="calc" style="float: right;"&gt;
                                &lt;button class="btn-sm btn-info" id="calc-btn" onclick="$('#calc').window('open');"&gt;Calculator &lt;/button&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;div style="clear: both;"&gt;&lt;/div&gt;

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                        &lt;!-- Question 1 (Numerical) --&gt;
                        &lt;div class="question" data-answer="75.34" data-correct-score="1" data-incorrect-score="0" data-max="76" data-min="75" data-precision="2" data-subject="Stress and Strain" data-type="NAT" data-explanation="Tensile stress, σ = F / A, where F is the applied force and A is the cross-sectional area."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;1. A cylindrical rod with a diameter of 10 mm is subjected to an axial tensile force of 6 kN. Calculate the tensile stress (in MPa) in the rod. Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer1" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 2 (Multiple Select) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="1" data-incorrect-score="0" data-subject="Stress and Strain" data-type="MSQ" data-explanation="Stress is dependent on force and area, while strain is the result of deformation. Young's modulus relates stress and strain."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;2. Which of the following factors affect stress in a material?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options2" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Applied force&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options2" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Material density&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options2" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Cross-sectional area&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options2" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Young’s modulus&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 3 (MCQ) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Stress and Strain" data-type="MCQ" data-explanation="Shear stress occurs when a force is applied parallel to the surface of a material, as opposed to tensile stress, which acts perpendicular."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;3. Which type of stress occurs when a force is applied parallel to the surface of a material?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options3" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Tensile stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options3" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Shear stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options3" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Compressive stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options3" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Bending stress&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 4 (MCQ) --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Stress and Strain" data-type="MCQ" data-explanation="Poisson’s ratio defines the relationship between longitudinal and lateral strain in a material subjected to axial stress."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;4. What is Poisson’s ratio a measure of in materials?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options4" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Longitudinal stress to lateral stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options4" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Longitudinal strain to lateral strain&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options4" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Lateral stress to longitudinal stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options4" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Lateral strain to longitudinal strain&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 5 (Numerical) --&gt;
                        &lt;div class="question" data-answer="0.002" data-correct-score="1" data-incorrect-score="0" data-max="0.003" data-min="0.001" data-precision="3" data-subject="Stress and Strain" data-type="NAT" data-explanation="Strain, ε = ΔL / L, where ΔL is the change in length and L is the original length."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;5. A steel bar 1 meter long is subjected to a tensile load, causing it to extend by 2 mm. Calculate the strain in the bar. Use three decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer5" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 6 (MSQ) --&gt;
                        &lt;div class="question" data-answer="A;D" data-correct-score="1" data-incorrect-score="0" data-subject="Stress and Strain" data-type="MSQ" data-explanation="Hooke’s Law relates stress and strain within the elastic limit. The modulus of elasticity is a measure of stiffness and determines how much a material deforms under stress."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;6. Which of the following statements are true regarding the elastic behavior of materials?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options6" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Hooke’s Law is valid within the elastic limit&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options6" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Elastic deformation is permanent&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options6" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Strain is independent of stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options6" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;The modulus of elasticity is a measure of stiffness&lt;/label&gt;&lt;/div&gt; 
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 7 (Numerical) --&gt;
                        &lt;div class="question" data-answer="200" data-correct-score="1" data-incorrect-score="0" data-max="205" data-min="195" data-precision="0" data-subject="Stress and Strain" data-type="NAT" data-explanation="Modulus of elasticity, E = σ / ε, where σ is the stress and ε is the strain."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;7. A material experiences a stress of 200 MPa and strain of 0.001. Calculate the modulus of elasticity (in GPa). Use whole numbers only.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer7" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 8 (MCQ) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Stress and Strain" data-type="MCQ" data-explanation="In the plastic region of a stress-strain curve, materials experience permanent deformation, and the relationship between stress and strain is no longer linear."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;8. What happens to a material in the plastic region of the stress-strain curve?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The material behaves elastically&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Stress and strain remain proportional&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The material undergoes permanent deformation&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The material has reached its fracture point&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 9 (Multiple Select) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="0" data-subject="Stress and Strain" data-type="MSQ" data-explanation="Strain hardening increases the material’s strength and ductility through plastic deformation, while necking leads to localized reduction in cross-section before failure."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;9. Which of the following phenomena occur in the plastic region of a material under tension?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options9" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Strain hardening&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options9" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Elastic recovery&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options9" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Necking&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options9" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Brittle fracture&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 10 (MCQ) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Stress and Strain" data-type="MCQ" data-explanation="Yield stress is the point at which a material transitions from elastic deformation to plastic deformation, beyond which permanent deformation occurs."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;10. The stress at which a material begins to deform plastically is called:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options10" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Ultimate stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options10" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Yield stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options10" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Fracture stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options10" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Tensile stress&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 11 (Numerical) --&gt;
                        &lt;div class="question" data-answer="250" data-correct-score="1" data-incorrect-score="0" data-max="260" data-min="240" data-precision="0" data-subject="Stress and Strain" data-type="NAT" data-explanation="Stress, σ = F / A, where F is the applied force, and A is the cross-sectional area."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;11. A steel rod with a cross-sectional area of 50 mm² is subjected to a tensile force of 12.5 kN. Calculate the tensile stress in the rod (in MPa). Use whole numbers only.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer11" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 12 (MSQ) --&gt;
                        &lt;div class="question" data-answer="B;D" data-correct-score="2" data-incorrect-score="0" data-subject="Stress and Strain" data-type="MSQ" data-explanation="Hooke’s Law applies in the elastic region, and necking happens after the ultimate tensile strength is reached. Elastic recovery occurs when the material returns to its original shape after the load is removed."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;12. Which of the following phenomena occur in the elastic region of the stress-strain curve?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options12" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Strain hardening&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options12" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Elastic recovery&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options12" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Necking&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options12" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Hooke’s Law applies&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 13 (Numerical) --&gt;
                        &lt;div class="question" data-answer="180" data-correct-score="1" data-incorrect-score="0" data-max="180" data-min="180" data-precision="0" data-subject="Stress and Strain" data-type="NAT" data-explanation="Compressive stress, σ = F / A, where F is the applied force and A is the cross-sectional area."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;13. A column with a cross-sectional area of 100 mm² is subjected to a compressive load of 18 kN. Calculate the compressive stress in the column (in MPa). Use whole numbers only.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer13" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 14 (MCQ) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-subject="Stress and Strain" data-type="MCQ" data-explanation="Ductile materials exhibit large strains and can deform significantly before failure, while brittle materials fracture with little or no plastic deformation."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;-0.33&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;14. Which of the following materials is likely to exhibit large strains before failure?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options14" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Brittle material&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options14" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Glass&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options14" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Ductile material&lt;/label&gt;&lt;/div&gt;
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                        &lt;!-- Question 16 (MCQ) --&gt;
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                            &lt;p&gt;16. Which phenomenon describes the failure of a material due to repeated cyclic loading?&lt;/p&gt;
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                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            }

            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/stress-strain.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-359937521006941932</guid><pubDate>Sun, 27 Oct 2024 17:07:00 +0000</pubDate><atom:updated>2025-03-23T15:16:13.928+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Torsion</title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Torsion Topic-wise Online Quiz&lt;/title&gt;
      &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
        &lt;!-- &lt;link href="quiz.css" rel="stylesheet"&gt; --&gt;
        &lt;meta charset="UTF-8"&gt;&lt;/meta&gt;
        &lt;meta content="width=device-width, initial-scale=1.0" name="viewport"&gt;&lt;/meta&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        
        &lt;style&gt;
          .col-lg-3{
            display:none;
          }
          .col-lg-9{
            flex: 0 0 100%;
          }
            .container{
	            padding:5px;
            }

            img{
            
            border:0px;
            }
            /* .options{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            } */
            .options div{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            }

            #question-container{
            
                padding:4px;
                height:35%;
                overflow-y:auto;
                padding-bottom: 100px;
                
            }
            
            #footer_buttons{
                display: none;
                position:fixed;
                bottom:0px;
                background:#ffffff;
                width:100%;
                height:80px;
                padding:4px;		
                border-top:1px solid #dddddd;
            }
            /* .question-info{
                margin: 5px auto;
                padding: 5px 0px 20px;
                border-bottom: 1px solid #CECECE;
                overflow-y: auto;
            } */
            #fullscreen-container row{
                margin-right: -15px;
                margin-left: -15px;
                display: flex;
                gap:15px;
                width: 100%;
            }
            #fullscreen-container row col-md-8, col-md-4{
                position: relative;
                min-height: 1px;
                padding-left: 15px;
                padding-right: 15px;
            }
            #fullscreen-container row col-md-8{
                float:left;
                width: 66.66666667%;
            }
            #fullscreen-container  row col-md-4{
                float:right;
                width: 33.33333333%;
            }
            .container-fluid{
                padding-left: 15px;
                padding-right: 15px;
                margin-left: auto;
                margin-right: auto;
            }
            #fullscreen-container{
                display: none;
                background-color: #ffffff;
                overflow: auto;
            }
            .quiz-attempt-inline-block{
                display: inline-block;
                width: 180px;
            }
         	#fullscreen-container .question-palette button {
              width: 40px;
              margin: 5px;
              padding: 5px;
            }
            @media(max-width:900px){
               #fullscreen-container button #confirmSubmit #cancelSubmit #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                gap:10px;
                font-size: 12px;
            }
                #fullscreen-container .row .col-md-4 .col-md-8 .options{
                    font-size: 12px;
                }
                #fullscreen-container .col-md-4{
                    width: 33.33333333%;
                }
                #fullscreen-container .col-md-8{
                    width: 66.66666667%;
                }
                 #fullscreen-container #footer_buttons{
                    bottom:0px;
                  	height:auto;
                }

                #fullscreen-container.quiz-attempt-inline-block{
                    display: flex;
                }
                #answered-count, #unanswered-count,#review-count,#not-visited-count {
                    width:20px;
                    margin: 5px;
                    padding: 5px;
                }
                #fullscreen-container h1 p{
                    font-size: 12px;
                }
              
                #fullscreen-container .question-palette h3{
                  font-size:14px;
                  font-weight:bold;
                }
                #calc-container {
                  position: absolute;
                  top: 30%;
                  left: 50%;
              	}
            }

            .angled-text {
                text-align: center;
                transform: rotate(-45deg);
                font-size: 44px;
                font-weight: bolder;
                color: rgba(19, 17, 17, 0.352);
                z-index: 1;
            }




        &lt;/style&gt;

        &lt;style&gt;
            body {
                font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
                margin: 0;
                padding: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #333;
                background-color: #f2f2f2;
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            /* #cont, #quiz-container, #container {
                background-color: #fff;
            }

            #cont {
                overflow: auto;
                height: 100vh;
                flex-wrap: wrap;
                flex-direction: row;
            } */
/* 
            .question {
                margin-top: 10px;
                padding: 10px;
                overflow-y: auto;
                display: none;
                width: 70%;
                margin-bottom: 20px;
            } */

            h1, p {
                font-size: 16px;
                margin-top: 20px;
                color: #333;
            }

            .options {
                display: flex;
                flex-direction: column;
                flex-wrap: wrap;
                gap: 10px;
            }

            .options div {
                display: flex;
                align-items: center;
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            label {
                margin-left: 5px;
                font-size: 14px;
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            input[type="radio"], input[type="checkbox"] {
                padding: 8px;
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            button, #confirmSubmit, #cancelSubmit, #submit-user-info {
                display: inline-block;
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            #submit {
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            #score-summary tbody tr:hover {
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            .question-palette {
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            .question-palette button {
                margin: 10px;
                padding: 10px;
                border: 1px solid #ccc;
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                color: white;
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            .correct-answer {
                background-color: #71ba5d;
                color: white;
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            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
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            .not-answered {
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            table {
                width: 100%;
                border-collapse: collapse;
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            th, td {
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            th {
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            .category-row {
                background-color: #e0f7fa; /* Light cyan */
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            .total-row {
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            .modal, .admodal {
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
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                width: 100%;
                height: 100%;
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            .modal-content, .admodal-content {
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                flex-direction: column;
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                  position: absolute;
                  top: 30%;
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            #detailed-results .question-result{
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              padding:20px;
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            #detailed-results h3{
            text-align:center; 
            font-size:25px; 
            font-weight:bold;
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        &lt;/style&gt;
    &lt;/head&gt;
    &lt;body&gt;
        &lt;div id="user-info"&gt;
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                &lt;h1&gt;Enter Your Details&lt;/h1&gt;
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        &lt;/div&gt;
      
        &lt;div id="start-page" style="display: none;"&gt;
          &lt;center&gt;&lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;&lt;/center&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
            &lt;p&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;
                &lt;li&gt;The total duration of the examination is 45 minutes .&lt;/li&gt;
                &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
                &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
            &lt;/ol&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;To answer a question, do the following:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;&lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;&lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;&lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;               
            &lt;li&gt;
            You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;&lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To select your answer, click on the button on one of the options&lt;/li&gt;&lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;&lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next &lt;/b&gt;button&lt;/li&gt;&lt;/ol&gt;&lt;li&gt;
            Procedure for answering a numerical answer type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;&lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;&lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;&lt;/ol&gt;  
            &lt;li&gt;
            To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;&lt;/ol&gt;&lt;ol style="text-align: left;"&gt;
            &lt;/ol&gt;
            &lt;center&gt;&lt;button id="start-button"&gt;Start Quiz&lt;/button&gt;&lt;/center&gt;
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                &lt;p&gt;Do you really want to submit this quiz?&lt;/p&gt;
                &lt;button id="confirmSubmit"&gt;Submit Quiz&lt;/button&gt;
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                                &lt;p&gt;Torsion&lt;/p&gt;
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                            &lt;b&gt;Time Left:
                                &lt;span id="timer"&gt;180:00&lt;/span&gt;
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                            &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
                          &lt;b&gt;&lt;h1&gt;AERO GATE TOPPER&lt;/h1&gt;&lt;/b&gt;
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                        &lt;b&gt;  &lt;/b&gt;
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                        &lt;!-- Question 1 (Numerical) --&gt;
                        &lt;div class="question" data-answer="120" data-correct-score="2" data-incorrect-score="0" data-max="125" data-min="115" data-precision="1" data-subject="Torsion" data-type="NAT" data-explanation="Angle of twist, θ = (T * L) / (G * J), where T is the applied torque, L is the length of the shaft, G is the shear modulus, and J is the polar moment of inertia."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;1. A solid circular shaft of 50 mm diameter and 1.2 m length is subjected to a torque of 300 Nm. If the shear modulus (G) is 80 GPa, calculate the angle of twist (in degrees). Use one decimal place.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer1" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 2 (Numerical) --&gt;
                        &lt;div class="question" data-answer="75.45" data-correct-score="2" data-incorrect-score="0" data-max="76" data-min="75" data-precision="2" data-subject="Torsion" data-type="NAT" data-explanation="Maximum shear stress, τ = (T * r) / J, where T is the torque, r is the outer radius of the shaft, and J is the polar moment of inertia for a hollow shaft: J = (π/32) * (D_o^4 - D_i^4)."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;2. A hollow circular shaft with outer diameter of 60 mm and inner diameter of 40 mm is subjected to a torque of 500 Nm. Calculate the maximum shear stress in the shaft (in MPa). Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer2" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 3 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Torsion" data-type="MCQ" data-explanation="In non-circular shafts, the torsional stiffness depends on the cross-sectional geometry, and the stress distribution is not uniform. The angle of twist is governed by the torsional stiffness, which is different from that of circular shafts."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;3. Which of the following statements is true about torsion in non-circular shafts?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options3" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Torsional stress is uniform along the shaft&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options3" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The shear modulus has no effect&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options3" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The angle of twist depends on the torsional stiffness&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options3" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The polar moment of inertia is irrelevant&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 4 (Numerical) --&gt;
                        &lt;div class="question" data-answer="12.80" data-correct-score="1" data-incorrect-score="0" data-max="13" data-min="12.5" data-precision="2" data-subject="Torsion" data-type="NAT" data-explanation="Power (P) = (T * ω) / 1000, where T is the torque and ω is the angular velocity in rad/s. ω = (2 * π * N) / 60, where N is the rotational speed in rpm."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;4. A shaft is transmitting 20 kW of power at 1500 rpm. Calculate the torque transmitted by the shaft (in Nm). Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer4" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 5 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="0" data-subject="Torsion" data-type="MSQ" data-explanation="The maximum shear stress in a shaft subjected to torsion depends on the applied torque and the polar moment of inertia of the shaft, which are essential in determining stress distribution."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;5. Which of the following factors affect the maximum shear stress in a shaft subjected to torsion?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options5" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;The applied torque&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options5" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;The modulus of elasticity&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options5" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;The polar moment of inertia&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options5" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Length of the shaft&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 6 (Numerical) --&gt;
                        &lt;div class="question" data-answer="28.45" data-correct-score="2" data-incorrect-score="0" data-max="29" data-min="28" data-precision="2" data-subject="Torsion" data-type="NAT" data-explanation="Angle of twist, θ = (T * L) / (G * J). The polar moment of inertia for a hollow shaft is: J = (π/32) * (D_o^4 - D_i^4), where D_o and D_i are the outer and inner diameters."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;6. A hollow circular shaft with an outer diameter of 80 mm and an inner diameter of 50 mm is 2 m long. If a torque of 600 Nm is applied and the shear modulus (G) is 75 GPa, calculate the angle of twist (in degrees). Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer6" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 7 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Torsion" data-type="MCQ" data-explanation="The polar moment of inertia represents the shaft's ability to resist torsional loads. It plays a key role in determining the amount of torsional deformation under applied torque."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;7. What does the polar moment of inertia in torsion problems indicate?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options7" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The ability to resist axial loads&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options7" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The ability to resist torsional loads&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options7" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The resistance to shear deformation&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options7" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The distribution of axial stresses&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 8 (Numerical) --&gt;
                        &lt;div class="question" data-answer="54.15" data-correct-score="2" data-incorrect-score="0" data-max="55" data-min="54" data-precision="2" data-subject="Torsion" data-type="NAT" data-explanation="Maximum shear stress, τ = (T * r) / J, where T is the applied torque, r is the outer radius of the shaft, and J is the polar moment of inertia for a hollow shaft: J = (π/32) * (D_o^4 - D_i^4)."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;8. A hollow circular shaft has an outer diameter of 90 mm and an inner diameter of 60 mm. If a torque of 800 Nm is applied, calculate the maximum shear stress in the shaft (in MPa). Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer8" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 9 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="A;D" data-correct-score="2" data-incorrect-score="0" data-subject="Torsion" data-type="MSQ" data-explanation="Torsional stiffness is influenced by the applied torque and the polar moment of inertia, which relates to the shaft's ability to resist torsional deformation."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;9. Which of the following parameters directly affect the torsional stiffness of a shaft?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options9" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;The applied torque&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options9" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;The length of the shaft&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options9" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;The material density&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options9" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;The polar moment of inertia&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 10 (Numerical) --&gt;
                        &lt;div class="question" data-answer="3.26" data-correct-score="1" data-incorrect-score="0" data-max="3.5" data-min="3.0" data-precision="2" data-subject="Torsion" data-type="NAT" data-explanation="Power (P) = (T * ω) / 1000, where T is the torque and ω is the angular velocity. ω = (2 * π * N) / 60, where N is the rotational speed in rpm."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;10. A shaft transmits a power of 50 kW at 2000 rpm. Calculate the torque transmitted by the shaft (in kNm). Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer10" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 11 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Torsion" data-type="MCQ" data-explanation="Solid circular shafts experience uniform stress distribution along the radius in torsion, while non-circular sections experience non-uniform stress distribution due to warping."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;11. Which of the following sections experiences uniform stress distribution under torsion?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options11" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Solid circular shaft&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options11" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Rectangular section&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options11" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Elliptical section&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options11" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;I-section&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 12 (Numerical) --&gt;
                        &lt;div class="question" data-answer="0.0025" data-correct-score="2" data-incorrect-score="0" data-max="0.003" data-min="0.002" data-precision="4" data-subject="Torsion" data-type="NAT" data-explanation="Strain energy stored in a shaft, U = (T² * L) / (2 * G * J), where T is the applied torque, L is the length of the shaft, G is the shear modulus, and J is the polar moment of inertia for a solid shaft: J = (π/32) * D⁴."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;12. A solid circular shaft of diameter 50 mm and length 1 m is subjected to a torque of 200 Nm. Calculate the strain energy stored in the shaft (in kJ). Use four decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer12" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 13 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Torsion" data-type="MCQ" data-explanation="Warping is a unique characteristic of torsion in non-circular sections, where the ends of the shaft twist in such a way that there is deformation along the length."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;13. Which of the following is a unique characteristic of torsion in non-circular sections?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options13" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Uniform shear stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options13" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Constant angle of twist&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options13" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Warping&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options13" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Constant polar moment of inertia&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 14 (Numerical) --&gt;
                        &lt;div class="question" data-answer="160" data-correct-score="1" data-incorrect-score="0" data-max="165" data-min="155" data-precision="1" data-subject="Torsion" data-type="NAT" data-explanation="Power (P) = (T * ω) / 1000, where T is the torque and ω is the angular velocity. ω = (2 * π * N) / 60, where N is the rotational speed in rpm."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
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                            &lt;/div&gt;
                            &lt;p&gt;14. A shaft transmits a power of 40 kW at 1200 rpm. Calculate the torque transmitted by the shaft (in Nm). Use one decimal place.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer14" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 15 (Theoretical) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Torsion" data-type="MCQ" data-explanation="In thin-walled sections, shear stress is concentrated along the walls, making the stress distribution non-uniform across the section. These sections can experience large deformations under torsion."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;15. In thin-walled sections under torsion, which of the following statements is true?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The shear stress is constant across the section&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options15" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The shear stress is concentrated along the walls&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The angle of twist remains constant&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;No warping occurs&lt;/label&gt;&lt;/div&gt;
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            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
         
            &lt;br /&gt;
            &lt;table&gt;
                &lt;thead&gt;
                    &lt;tr&gt;
                        &lt;th&gt;Subject&lt;/th&gt;
                        &lt;th&gt;Score&lt;/th&gt;
                        &lt;th&gt;Time Spent&lt;/th&gt;
                        &lt;th&gt;Correct&lt;/th&gt;
                        &lt;th&gt;Wrong&lt;/th&gt;
                        &lt;th&gt;Unattempted&lt;/th&gt;
                    &lt;/tr&gt;
                &lt;/thead&gt;
                &lt;tbody id="result-body"&gt;&lt;/tbody&gt;
            &lt;/table&gt;
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            
            &lt;!-- &lt;button id="restart" onclick="restartQuiz()"&gt;Restart Quiz&lt;/button --&gt;
            &lt;canvas height="200" id="timeSpentChart" width="400"&gt;&lt;/canvas&gt;
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            
            &lt;div id="detailed-results" style="left: 20px;"&gt;&lt;/div&gt;
            
            &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;&lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
        &lt;/div&gt;
        &lt;script&gt;
            let currentQuestionIndex = 0;
            let questions = [];
            let currentSubject = '';
            let timerInterval; 
            const questionStartTimes = [];
            let timeTakenArray = {};
            let subjectData = {};
            let userName = '';
            let countdownMinutes = 45;
            let countdownSeconds = countdownMinutes * 60;
            let targetTime;
            document.getElementById("registrationForm").addEventListener("submit", function(e) {
              e.preventDefault();
              var formData = new FormData(this);
              userName = formData.get('username');

              // Hide user-info and show start-page immediately
              document.getElementById('user-info').style.display = 'none';
              document.getElementById('start-page').style.display = 'block';

              fetch("https://script.google.com/macros/s/AKfycbyrfDJmI2KwyzUJOY8yCTTpuHIuqSLu2gbGPC0q8Lvqd7GeURM9PjqtKjXXkG9E14dO/exec", {
                  method: "POST",
                  body: formData
              })
              .then(response =&gt; response.json())
              .then(data =&gt; {
                  if (!data.success) {
                      alert("Error: " + data.error);
                      // Optionally show the user-info back if there was an error
                      document.getElementById('user-info').style.display = 'block';
                      document.getElementById('start-page').style.display = 'none';
                  }
              })
              .catch(error =&gt; {
                  console.error("Fetch error:", error);
                  alert("There was an error processing your request.");
                  // Optionally show the user-info back if there was an error
                  document.getElementById('user-info').style.display = 'block';
                  document.getElementById('start-page').style.display = 'none';
              });
          });
            
            document.getElementById('calc-btn').addEventListener('click', function () {
                const calcContainer = document.getElementById('calc-container');
                if (calcContainer.style.display === 'none' || calcContainer.style.display === '') {
                    calcContainer.style.display = 'block';
                } else {
                    calcContainer.style.display = 'none';
                }
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.appendChild(calcContainer);
            });

            const calcContainer = document.getElementById('calc-container');
            let offsetX, offsetY, isDragging = false;
            calcContainer.style.position = 'absolute';

            calcContainer.addEventListener('mousedown', (e) =&gt; {
                isDragging = true;
                offsetX = e.clientX - calcContainer.getBoundingClientRect().left;
                offsetY = e.clientY - calcContainer.getBoundingClientRect().top;
                document.addEventListener('mousemove', moveAt);
            });

            document.addEventListener('mouseup', () =&gt; {
                if (isDragging) {
                    isDragging = false;
                    document.removeEventListener('mousemove', moveAt);
                }
            });

            function moveAt(e) {
                if (isDragging) {
                    const newLeft = e.clientX - offsetX;
                    const newTop = e.clientY - offsetY;
                    calcContainer.style.left = newLeft + 'px';
                    calcContainer.style.top = newTop + 'px';
                }
            }

            function initializeSubjectData() {
                const questionElements = document.querySelectorAll('.question');
                questionElements.forEach((question) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjectData[subject]) {
                        subjectData[subject] = {
                            markedForReview: new Set(),
                            answeredQuestions: new Set(),
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            totalQuestions: 0
                        };
                    }
                    timeTakenArray[subject] = [];
                    subjectData[subject].totalQuestions++;
                });
            }

            document.getElementById('start-button').onclick = function() {
                document.getElementById('start-page').style.display = 'none';
                document.getElementById('fullscreen-container').style.display = 'block';
                startQuiz();
            };

            function startQuiz() {
                initializeSubjectData();
                showSubject('Torsion');
                questionStartTimes[currentQuestionIndex] = Date.now();
                startCountdown();
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                document.addEventListener('keydown', function(event) {
                    event.preventDefault();
                });
                document.addEventListener('contextmenu', function(e) {
                    e.preventDefault();
                });
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            }

            function showSubject(subject) {
                currentSubject = subject;
                questions = Array.from(document.querySelectorAll(`.question[data-subject="${subject}"]`));
                currentQuestionIndex = 0;
                updateQuestionDisplay();
                updateFooterButtons();
                updateQuestionPalette();
                questionStartTimes[currentQuestionIndex] = Date.now();
            }

            function updateQuestionDisplay() {
                document.querySelectorAll('.question').forEach((question) =&gt; {
                    question.style.display = 'none';
                });
                if (questions.length &gt; 0) {
                    questions[currentQuestionIndex].style.display = 'block';
                    if (questions[currentQuestionIndex].getAttribute('data-type') === 'NAT') {
                        document.getElementById('numeric-keypad').style.display = 'block';
                    } else {
                        document.getElementById('numeric-keypad').style.display = 'none';
                    }
                }
            }

            function updateFooterButtons() {
                document.getElementById('prev').style.display = currentQuestionIndex === 0 ? 'none' : 'inline';
                document.getElementById('next').style.display = currentQuestionIndex === questions.length - 1 ? 'none' : 'inline';
                document.getElementById('footer_buttons').style.display = questions.length &gt; 0 ? 'block' : 'none';
            }

            document.getElementById('prev').onclick = function(){
                if (currentQuestionIndex &gt; 0) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex--;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('next').onclick = function(){
                if (currentQuestionIndex &lt; questions.length - 1) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex++;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('clear').onclick = function(){
                const currentQuestion = questions[currentQuestionIndex];
                currentQuestion.querySelectorAll('input:checked').forEach(input =&gt; input.checked = false);
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                
                updateQuestionPalette();
            }

            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestionIndex];
                const timeTaken = (questionEndTime - questionStartTime) / 1000;
                const subject = currentSubject;            
                if (!timeTakenArray[subject]) {
                    timeTakenArray[subject] = {};
                }
                if (!timeTakenArray[subject][currentQuestionIndex]) {
                    timeTakenArray[subject][currentQuestionIndex] = 0;
                }
                timeTakenArray[subject][currentQuestionIndex] += timeTaken;
                questionStartTimes[currentQuestionIndex] = questionEndTime;
            }

            document.getElementById('submit').onclick = function(){
                recordTimeTaken();
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';    
                document.getElementById('confirmSubmit').onclick = function() {
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    modal.style.display = 'none';    
                    const adModal = document.getElementById('adModal');
                    const adCloseButton = document.getElementById('adClose');
                    adModal.style.display = 'block';    
                    setTimeout(() =&gt; {
                        adCloseButton.style.display = 'inline';
                    }, 5000);    
                    adCloseButton.onclick = function() {
                        adModal.style.display = 'none';
                        displayResults(); // Ensure this function is called to show results
                    };    
                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block'; // Show result container
                            showResult(); // Ensure this function is called to show results
                        }
                    }, 10000);    
                    clearInterval(timerInterval);
                };    
                document.getElementById('cancelSubmit').onclick = function() {
                    modal.style.display = 'none';
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                };    
                const exitFullScreen = document.exitFullscreen || document.mozCancelFullScreen || document.webkitExitFullscreen || document.msExitFullscreen;
                if (exitFullScreen) exitFullScreen.call(document);
            }

            function displayResults() {
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('user-name-display').innerText = userName;
                showResult();
                // window.location.href = './results.html'; 
            }

            document.getElementById('mark-for-review').onclick = function()  {
                const subjectMarks = subjectData[currentSubject].markedForReview;
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                if (subjectMarks.has(currentQuestionIndex)) {
                    subjectMarks.delete(currentQuestionIndex);
                } else {
                    subjectMarks.add(currentQuestionIndex);
                }
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }
                updateQuestionPalette();
            }

            function handleQuestionStateBeforeChange() {
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);

                // Save the user's answer
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }

                // Always mark the question as seen
                markAsSeen(currentQuestionIndex);
            }

            function updateQuestionStats() {
                // Count answered questions (green buttons)
                const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'green').length;

                // Count marked for review questions (orange buttons)
                const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'orange').length;

                // Total questions in the current subject
                const totalQuestions = questions.length;

                // Count unanswered questions (red buttons)
                const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'red').length;

                // Count not visited questions (black buttons)
                const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'black').length;

                // Update the counts in the HTML
                document.getElementById('answered-count').textContent = `${answeredCount}`;
                document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
                document.getElementById('review-count').textContent = `${markedForReviewCount}`;
                document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
            }

            function updateQuestionPalette() {
                const palette = document.getElementById('question-palette');
                palette.innerHTML = '';
                palette.appendChild(document.createElement('br'));
                palette.appendChild(document.createElement('hr'));
                const subjectHeading = document.createElement('h3');
                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            }

            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/torsion.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-1216808559084987742</guid><pubDate>Sun, 27 Oct 2024 17:04:00 +0000</pubDate><atom:updated>2025-03-23T15:17:43.658+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Unsymmetrical Bending</title><description>&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Unsymmetrical Bending Topic-wise Online Quiz&lt;/title&gt;
      &lt;img src="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s293" style="width: 100px;"/&gt;
        &lt;!-- &lt;link href="quiz.css" rel="stylesheet"&gt; --&gt;
        &lt;meta charset="UTF-8"&gt;&lt;/meta&gt;
        &lt;meta content="width=device-width, initial-scale=1.0" name="viewport"&gt;&lt;/meta&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        
        &lt;style&gt;
          .col-lg-3{
            display:none;
          }
          .col-lg-9{
            flex: 0 0 100%;
          }
            .container{
	            padding:5px;
            }

            img{
            
            border:0px;
            }
            /* .options{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            } */
            .options div{		
                padding:4px;
                height:65%;
                overflow-y:auto;
                
            }

            #question-container{
            
                padding:4px;
                height:35%;
                overflow-y:auto;
                padding-bottom: 100px;
                
            }
            
            #footer_buttons{
                display: none;
                position:fixed;
                bottom:0px;
                background:#ffffff;
                width:100%;
                height:80px;
                padding:4px;		
                border-top:1px solid #dddddd;
            }
            /* .question-info{
                margin: 5px auto;
                padding: 5px 0px 20px;
                border-bottom: 1px solid #CECECE;
                overflow-y: auto;
            } */
            #fullscreen-container row{
                margin-right: -15px;
                margin-left: -15px;
                display: flex;
                gap:15px;
                width: 100%;
            }
            #fullscreen-container row col-md-8, col-md-4{
                position: relative;
                min-height: 1px;
                padding-left: 15px;
                padding-right: 15px;
            }
            #fullscreen-container row col-md-8{
                float:left;
                width: 66.66666667%;
            }
            #fullscreen-container  row col-md-4{
                float:right;
                width: 33.33333333%;
            }
            .container-fluid{
                padding-left: 15px;
                padding-right: 15px;
                margin-left: auto;
                margin-right: auto;
            }
            #fullscreen-container{
                display: none;
                background-color: #ffffff;
                overflow: auto;
            }
            .quiz-attempt-inline-block{
                display: inline-block;
                width: 180px;
            }
         	#fullscreen-container .question-palette button {
              width: 40px;
              margin: 5px;
              padding: 5px;
            }
            @media(max-width:900px){
               #fullscreen-container button #confirmSubmit #cancelSubmit #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                gap:10px;
                font-size: 12px;
            }
                #fullscreen-container .row .col-md-4 .col-md-8 .options{
                    font-size: 12px;
                }
                #fullscreen-container .col-md-4{
                    width: 33.33333333%;
                }
                #fullscreen-container .col-md-8{
                    width: 66.66666667%;
                }
                 #fullscreen-container #footer_buttons{
                    bottom:0px;
                  	height:auto;
                }

                #fullscreen-container.quiz-attempt-inline-block{
                    display: flex;
                }
                #answered-count, #unanswered-count,#review-count,#not-visited-count {
                    width:20px;
                    margin: 5px;
                    padding: 5px;
                }
                #fullscreen-container h1 p{
                    font-size: 12px;
                }
              
                #fullscreen-container .question-palette h3{
                  font-size:14px;
                  font-weight:bold;
                }
                #calc-container {
                  position: absolute;
                  top: 30%;
                  left: 50%;
              	}
            }

            .angled-text {
                text-align: center;
                transform: rotate(-45deg);
                font-size: 44px;
                font-weight: bolder;
                color: rgba(19, 17, 17, 0.352);
                z-index: 1;
            }




        &lt;/style&gt;

        &lt;style&gt;
            body {
                font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
                margin: 0;
                padding: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #333;
                background-color: #f2f2f2;
            }

            /* #cont, #quiz-container, #container {
                background-color: #fff;
            }

            #cont {
                overflow: auto;
                height: 100vh;
                flex-wrap: wrap;
                flex-direction: row;
            } */
/* 
            .question {
                margin-top: 10px;
                padding: 10px;
                overflow-y: auto;
                display: none;
                width: 70%;
                margin-bottom: 20px;
            } */

            h1, p {
                font-size: 16px;
                margin-top: 20px;
                color: #333;
            }

            .options {
                display: flex;
                flex-direction: column;
                flex-wrap: wrap;
                gap: 10px;
            }

            .options div {
                display: flex;
                align-items: center;
            }

            label {
                margin-left: 5px;
                font-size: 14px;
                color: #333;
            }

            input[type="radio"], input[type="checkbox"] {
                padding: 8px;
                margin-bottom: 10px;
                border: 1px solid #ccc;
                border-radius: 3px;
            }

            input[type="radio"]:focus, input[type="checkbox"]:focus {
                outline: none;
                border-color: #007bff;
            }

            button, #confirmSubmit, #cancelSubmit, #submit-user-info {
                display: inline-block;
                padding: 6px 12px;
                margin-left: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #fff;
                border: none;
                background-color: #0056b3;
                border-radius: 4px;
                cursor: pointer;
                transition: background-color 0.3s ease;
            }

            button:hover, #submit-user-info:hover {
                background-color: #0056b3;
            }

            #confirmSubmit {
                background-color: #5bc0de;
            }

            #confirmSubmit:hover {
                background-color: #3fb5da;
            }

            #cancelSubmit {
                background-color: #d9534f;
            }

            #cancelSubmit:hover {
                background-color: #d43f3a;
            }

            #clear, #prev, #next, #mark-for-review, #submit {
                padding: 10px 20px;
                border-radius: 4px;
                cursor: pointer;
            }

            #prev, #next {
                background-color: #5cb85c;
            }

            #prev:hover, #next:hover {
                background-color: #4cae4c;
            }

            #mark-for-review {
                background-color: #f0ad4e;
            }

            #submit {
                background-color: #d9534f;
            }

            #submit:hover {
                background-color: #d43f3a;
            }

            /* #result {
                text-align: center;
                font-size: 20px;
                font-weight: bold;
                margin-top: 20px;
            }

            #score-summary {
                width: 95%;
                border-collapse: collapse;
                margin-top: 20px;
                margin-bottom: 20px;
            }

            #score-summary th, #score-summary td {
                padding: 10px;
                text-align: center;
            }

            #score-summary tbody tr:nth-child(odd) {
                background-color: #f9f9f9;
            }

            #score-summary tbody tr:hover {
                background-color: #e0e0e0;
            } */

            #user-info {
                max-width: 400px;
                margin: 0 auto;
                padding: 20px;
                background-color: #f9f9f9;
                border-radius: 8px;
                box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
                text-align: center;
            }

            #user-info input[type="text"], #user-info input[type="email"] {
                width: 90%;
                padding: 10px;
                margin-bottom: 15px;
                border: 2px solid #ccc;
                border-radius: 4px;
                font-size: 16px;
            }

            #user-info input[type="text"]:focus, #user-info input[type="email"]:focus {
                border-color: #007bff;
                box-shadow: 0 0 5px rgba(0, 123, 255, 0.5);
            }

            .question-palette {
                background-color: #fff;
            }

            .question-palette button {
                margin: 10px;
                padding: 10px;
                border: 1px solid #ccc;
                background-color: black;
                color: white;
            }

            .correct-answer {
                background-color: #71ba5d;
                color: white;
            }

            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
            }

            .not-answered {
                background-color: #fff;
                color: black;
            }

            table {
                width: 100%;
                border-collapse: collapse;
                margin-bottom: 20px;
            }

            th, td {
                border: 1px solid #ddd;
                padding: 8px;
            }

            th {
                background-color: #f2f2f2;
                text-align: left;
                font-weight: bold;
            }

            .category-row {
                background-color: #e0f7fa; /* Light cyan */
            }

            .total-row {
                background-color: #ffe0b2; /* Light orange */
            }

            .modal, .admodal {
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
                top: 0;
                width: 100%;
                height: 100%;
                background-color: rgba(0, 0, 0, 0.4);
            }

            .modal-content, .admodal-content {
                background-color: white;
                margin: 15% auto;
                padding: 20px;
                border: 1px solid #888;
                width: 80%;
                max-width: 400px;
                text-align: center;
                border-radius: 5px;
            }

            .adclose {
                color: #aaa;
                float: right;
                font-size: 28px;
                font-weight: bold;
            }

            .adclose:hover, .adclose:focus {
                color: black;
                cursor: pointer;
            }

            #start-page {
                display: none;
                padding: 20px;
                background-color: #fff;
            }

            #start-button {
                display: inline-block;
                padding: 10px;
                font-size: 18px;
                background-color: #007bff;
                color: #fff;
            }
              #numeric-keypad {                
                margin-top:50px;
                background-color: #f9f9f9;
                box-shadow: 0 -2px 10px rgba(0, 0, 0, 0.2);
                padding: 10px; 
                z-index: 1000;
              }

              #numeric-keypad .options {
                  display: flex;
                  flex-direction: column;
                  align-items: center;
              }

              #numeric-keypad h3 {
                  margin: 0 0 10px; 
              }

              #numeric-keypad div {
                  display: flex;
                  justify-content: center;
                  margin-bottom: 5px;
              }

              #numeric-keypad button {
                  background-color: #4185f2;
                width:30px;
                  color: white;
                  border: none;
                  border-radius: 5px;
                  padding: 10px;
                  font-size: 15px;
                  margin: 0 5px;
                  cursor: pointer;
                  transition: background-color 0.3s;
              }

              #numeric-keypad button:hover {
                  background-color: #0056b3;
              }

              #numeric-keypad button:active {
                  background-color: #004080;
              }

            @media screen and (max-width: 900px) {
                body, p, label {
                    font-size: 14px;
                }

                .question-palette button {
                    text-align: center;
                }
            }
            .question-info {
                display: flex;
                flex-direction: column;
                gap: 10px; /* Adjust the spacing between elements */
            }

            #calc-container {
                  position: absolute;
                  top: 30%;
                  margin-left: 50%;
            }
            #detailed-results .question-result{
              padding:30px;
              border: 2px solid black;
            }
            #detailed-results{
              left: 20px; 
              padding:20px;
            }
            #detailed-results h3{
            text-align:center; 
            font-size:25px; 
            font-weight:bold;
            }
        &lt;/style&gt;
    &lt;/head&gt;
    &lt;body&gt;
        &lt;div id="user-info"&gt;
          &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
                data-ad-format="fluid"
                data-ad-client="ca-pub-2922315402866630"
                data-ad-slot="4993484640"&gt;
            &lt;/ins&gt;
            &lt;script&gt;
                (adsbygoogle = window.adsbygoogle || []).push({});
            &lt;/script&gt;
            &lt;form id="registrationForm"&gt;            
                &lt;h1&gt;Enter Your Details&lt;/h1&gt;
               	&lt;input type="hidden" id="password" name="password" value="Unsymmetrical Bending" /&gt;
                &lt;label for="name"&gt;Name:&lt;/label&gt;
                &lt;input id="username" name="username" required="" type="text" /&gt;
                &lt;!-- &lt;label for="email"&gt;Email:&lt;/label&gt;
                &lt;input id="email" name="email" required="" type="email" /&gt; --&gt;
                &lt;button type="submit" id="submit-user-info"&gt;Next&lt;/button&gt;
            &lt;/form&gt;
             &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630" crossorigin="anonymous"&gt;&lt;/script&gt;
            &lt;ins class="adsbygoogle"
                style="display:block; text-align:center;"
                data-ad-layout="in-article"
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                          &lt;b&gt;&lt;h1&gt;AERO GATE TOPPER&lt;/h1&gt;&lt;/b&gt;
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                        &lt;!-- Question 1 (Hard) --&gt;
                        &lt;div class="question" data-answer="45.0" data-correct-score="2" data-incorrect-score="0" data-max="50" data-min="40" data-precision="1" data-subject="Unsymmetrical Bending" data-type="NAT" data-explanation="The neutral axis is shifted due to the bending moment applied at an angle to the principal axis, calculated using the moments of inertia and bending moment direction."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;1. A rectangular beam has a width of 100 mm and height of 200 mm. If a bending moment of 500 Nm is applied at an angle of 30° to the principal axis, calculate the angle of the neutral axis with respect to the principal axis (in degrees). Use one decimal place.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer1" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 2 (Hard) --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.66" data-subject="Unsymmetrical Bending" data-type="MCQ" data-explanation="In unsymmetrical bending, the orientation of the neutral axis depends on the moments of inertia about the principal axes. The neutral axis shifts in response to the applied bending moment."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.66&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;2. In unsymmetrical bending, the orientation of the neutral axis depends on:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;The area of the cross-section&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;The moments of inertia about the principal axes&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options2" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The applied torque&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;The modulus of elasticity&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 3 (Moderate) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="0" data-subject="Unsymmetrical Bending" data-type="MSQ" data-explanation="In unsymmetrical bending, the bending stress distribution becomes non-linear, and the neutral axis shifts due to the non-coincidence of the load with the principal axes."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;3. Which of the following are primary effects of unsymmetrical bending in a beam?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options3" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Bending stress distribution becomes non-linear&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options3" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;Shear stress remains constant&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options3" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;The neutral axis shifts&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options3" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;No shift in neutral axis&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 4 (Hard) --&gt;
                        &lt;div class="question" data-answer="5.67" data-correct-score="2" data-incorrect-score="0" data-max="6" data-min="5" data-precision="2" data-subject="Unsymmetrical Bending" data-type="NAT" data-explanation="The stress in the beam due to unsymmetrical bending is calculated using the applied bending moment, the principal moments of inertia, and the distance from the neutral axis."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt;| Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;4. A beam is subjected to a bending moment of 200 Nm along an axis at 45° to its principal axes. The principal moments of inertia are 3000 mm⁴ and 1500 mm⁴, respectively. Calculate the stress at a point located 50 mm from the neutral axis (in MPa). Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer4" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 5 (Moderate) --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Unsymmetrical Bending" data-type="MCQ" data-explanation="The analysis of unsymmetrical bending requires resolution into the principal moments of inertia to determine stress distribution and deflections."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;5. Which of the following is the correct approach to analyze unsymmetrical bending in beams?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Euler's formula for buckling&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Principal stress theory&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Mohr's circle for plane stress&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;Resolution into components of moments of inertia&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 6 (Hard) --&gt;
                        &lt;div class="question" data-answer="7.12" data-correct-score="3" data-incorrect-score="0" data-max="7.20" data-min="7.00" data-precision="2" data-subject="Unsymmetrical Bending" data-type="NAT" data-explanation="The bending stress is calculated using the bending moment, moments of inertia, and the distance from the neutral axis. The angle of the applied moment with the principal axis causes unsymmetrical stress distribution."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;3&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;6. A beam experiences a bending moment of 300 Nm, applied at 60° to the principal axis. The moments of inertia are 2500 mm⁴ and 1500 mm⁴. Calculate the bending stress (in MPa) at a distance of 50 mm from the neutral axis. Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer6" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 7 (Moderate) --&gt;
                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Unsymmetrical Bending" data-type="MSQ" data-explanation="The neutral axis in unsymmetrical bending is influenced by the moments of inertia about the principal axes and shifts depending on the direction of the applied moment."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;7. Which of the following statements are true regarding the location of the neutral axis in unsymmetrical bending?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options7" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;It is determined by the moments of inertia about the principal axes&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option2" name="msq-options7" type="checkbox" value="B" /&gt;&lt;label for="msq-option2"&gt;It remains fixed regardless of load direction&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options7" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;It shifts depending on the applied moment direction&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options7" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;It always coincides with the centroidal axis&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 8 (Hard) --&gt;
                        &lt;div class="question" data-answer="55.43" data-correct-score="2" data-incorrect-score="0" data-max="56" data-min="55" data-precision="2" data-subject="Unsymmetrical Bending" data-type="NAT" data-explanation="The maximum bending stress is calculated using the bending moment, moments of inertia, and the distance from the neutral axis. Unsymmetrical loading causes stress variation along the cross-section."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;8. For a beam with an unsymmetrical cross-section, the moments of inertia are 5000 mm⁴ and 3000 mm⁴. If the beam is subjected to a bending moment of 400 Nm, calculate the maximum bending stress (in MPa) at a point 75 mm away from the neutral axis. Use two decimal places.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer8" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 9 (Moderate) --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-subject="Unsymmetrical Bending" data-type="MCQ" data-explanation="In an unsymmetrical loading condition, the bending moment vector does not align with the principal axes and is oriented at an angle to both the principal and neutral axes."&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;9. In an unsymmetrically loaded beam, the bending moment vector is oriented:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;&lt;input id="mcq-option1" name="mcq-options9" type="radio" value="A" /&gt;&lt;label for="mcq-option1"&gt;Perpendicular to the neutral axis&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option2" name="mcq-options9" type="radio" value="B" /&gt;&lt;label for="mcq-option2"&gt;Along the neutral axis&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options9" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;Parallel to the principal axis&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="mcq-option4" name="mcq-options9" type="radio" value="D" /&gt;&lt;label for="mcq-option4"&gt;At an angle to both principal and neutral axes&lt;/label&gt;&lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Question 10 (Hard) --&gt;
                        &lt;div class="question" data-answer="2.87" data-correct-score="2" data-incorrect-score="0" data-max="3.0" data-min="2.7" data-precision="2" data-subject="Unsymmetrical Bending" data-type="NAT" data-explanation="The deflection due to unsymmetrical bending is calculated by resolving the moments into components along the principal axes and using the appropriate moments of inertia."&gt;
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                            &lt;p&gt;10. A beam with unsymmetrical cross-section is subjected to a bending moment of 250 Nm. The moments of inertia about the principal axes are 4000 mm⁴ and 2000 mm⁴. Calculate the deflection at a point 80 mm away from the neutral axis (in mm). Use two decimal places.&lt;/p&gt;
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                            &lt;p&gt;11. A beam experiences a bending moment of 500 Nm applied at an angle of 45° to the principal axis. The moments of inertia are 4000 mm⁴ and 2000 mm⁴. Calculate the angle of deflection (in degrees) at a point 100 mm from the neutral axis. Use two decimal places.&lt;/p&gt;
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                        &lt;div class="question" data-answer="A;B" data-correct-score="2" data-incorrect-score="0" data-subject="Unsymmetrical Bending" data-type="MSQ" data-explanation="The principal stresses and strains caused by unsymmetrical bending are influenced by the distribution of stresses along the length of the beam and the direction of the bending moment."&gt;
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                            &lt;p&gt;12. Which of the following effects occur in a beam undergoing unsymmetrical bending?&lt;/p&gt;
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                                &lt;div&gt;&lt;input id="msq-option1" name="msq-options12" type="checkbox" value="A" /&gt;&lt;label for="msq-option1"&gt;Principal stresses develop along both axes&lt;/label&gt;&lt;/div&gt;
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                                &lt;div&gt;&lt;input id="msq-option3" name="msq-options12" type="checkbox" value="C" /&gt;&lt;label for="msq-option3"&gt;Shear stress remains uniform&lt;/label&gt;&lt;/div&gt;
                                &lt;div&gt;&lt;input id="msq-option4" name="msq-options12" type="checkbox" value="D" /&gt;&lt;label for="msq-option4"&gt;Neutral axis is unaffected&lt;/label&gt;&lt;/div&gt;
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                            &lt;p&gt;13. A beam with unsymmetrical cross-section is subjected to a bending moment of 300 Nm along an axis at 60° to the principal axis. The moments of inertia are 3500 mm⁴ and 2500 mm⁴. Calculate the deflection (in mm) at a point 120 mm away from the neutral axis. Use two decimal places.&lt;/p&gt;
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                                &lt;div&gt;&lt;input id="mcq-option3" name="mcq-options14" type="radio" value="C" /&gt;&lt;label for="mcq-option3"&gt;The angle and magnitude of the applied moment&lt;/label&gt;&lt;/div&gt;
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                        &lt;div class="question" data-answer="11.22" data-correct-score="2" data-incorrect-score="0" data-max="11.50" data-min="11.00" data-precision="2" data-subject="Unsymmetrical Bending" data-type="NAT" data-explanation="The maximum bending stress in unsymmetrical bending depends on the applied moment, the cross-sectional geometry, and the orientation of the moment relative to the principal axes."&gt;
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                            &lt;p&gt;15. A beam with moments of inertia 5000 mm⁴ and 3500 mm⁴ is subjected to a bending moment of 450 Nm at an angle of 45° to the principal axis. Calculate the maximum bending stress (in MPa) at a point 90 mm from the neutral axis. Use two decimal places.&lt;/p&gt;
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                const timeTaken = (questionEndTime - questionStartTime) / 1000;
                const subject = currentSubject;            
                if (!timeTakenArray[subject]) {
                    timeTakenArray[subject] = {};
                }
                if (!timeTakenArray[subject][currentQuestionIndex]) {
                    timeTakenArray[subject][currentQuestionIndex] = 0;
                }
                timeTakenArray[subject][currentQuestionIndex] += timeTaken;
                questionStartTimes[currentQuestionIndex] = questionEndTime;
            }

            document.getElementById('submit').onclick = function(){
                recordTimeTaken();
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';    
                document.getElementById('confirmSubmit').onclick = function() {
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    modal.style.display = 'none';    
                    const adModal = document.getElementById('adModal');
                    const adCloseButton = document.getElementById('adClose');
                    adModal.style.display = 'block';    
                    setTimeout(() =&gt; {
                        adCloseButton.style.display = 'inline';
                    }, 5000);    
                    adCloseButton.onclick = function() {
                        adModal.style.display = 'none';
                        displayResults(); // Ensure this function is called to show results
                    };    
                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block'; // Show result container
                            showResult(); // Ensure this function is called to show results
                        }
                    }, 10000);    
                    clearInterval(timerInterval);
                };    
                document.getElementById('cancelSubmit').onclick = function() {
                    modal.style.display = 'none';
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                };    
                const exitFullScreen = document.exitFullscreen || document.mozCancelFullScreen || document.webkitExitFullscreen || document.msExitFullscreen;
                if (exitFullScreen) exitFullScreen.call(document);
            }

            function displayResults() {
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('user-name-display').innerText = userName;
                showResult();
                // window.location.href = './results.html'; 
            }

            document.getElementById('mark-for-review').onclick = function()  {
                const subjectMarks = subjectData[currentSubject].markedForReview;
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                if (subjectMarks.has(currentQuestionIndex)) {
                    subjectMarks.delete(currentQuestionIndex);
                } else {
                    subjectMarks.add(currentQuestionIndex);
                }
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }
                updateQuestionPalette();
            }

            function handleQuestionStateBeforeChange() {
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);

                // Save the user's answer
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }

                // Always mark the question as seen
                markAsSeen(currentQuestionIndex);
            }

            function updateQuestionStats() {
                // Count answered questions (green buttons)
                const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'green').length;

                // Count marked for review questions (orange buttons)
                const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'orange').length;

                // Total questions in the current subject
                const totalQuestions = questions.length;

                // Count unanswered questions (red buttons)
                const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'red').length;

                // Count not visited questions (black buttons)
                const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'black').length;

                // Update the counts in the HTML
                document.getElementById('answered-count').textContent = `${answeredCount}`;
                document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
                document.getElementById('review-count').textContent = `${markedForReviewCount}`;
                document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
            }

            function updateQuestionPalette() {
                const palette = document.getElementById('question-palette');
                palette.innerHTML = '';
                palette.appendChild(document.createElement('br'));
                palette.appendChild(document.createElement('hr'));
                const subjectHeading = document.createElement('h3');
                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
                const detailedResultsContainer = document.getElementById('detailed-results');
                detailedResultsContainer.innerHTML = ''; // Clear previous results

                for (const subject in subjects) {
                    const subjectReport = subjects[subject];
                    const subjectDiv = document.createElement('div');
                    subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

                    let totalScore = 0; // Initialize total score

                    subjectReport.questions.forEach((questionDetail, index) =&gt; {
                        const userAnswer = questionDetail.userAnswer;
                        const questionType = questionDetail.type; // Ensure question type is captured properly
                        const isCorrect = questionDetail.result === 'Correct';
                        const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
                        const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

                        let correctAnswer = questionDetail.correctAnswer; // Default correct answer
                        let optionsHTML = '';

                        // Handle each question type properly
                        if (questionType === 'MCQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer === option ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'MSQ') {
                            optionsHTML = '&lt;div&gt;';
                            questionDetail.options.forEach((option) =&gt; {
                                const isChecked = userAnswer.includes(option) ? 'checked' : '';
                                optionsHTML += 
                                    `&lt;div&gt;
                                        &lt;label&gt;
                                            &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                                        &lt;/label&gt;
                                    &lt;/div&gt;`;
                            });
                            optionsHTML += '&lt;/div&gt;';
                        } else if (questionType === 'NAT') {
                            optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
                        }

                        // Extract explanation from the question element
                        // const explanation = questionDetail.explanation || "No explanation available.";
                       // const explanation = question.getAttribute('data-explanation');

                        // Create HTML for question details
                        const questionHTML = 
                            `&lt;div class="question-result ${backgroundClass}"&gt;
                                &lt;div class="question-meta"&gt;
                                    &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                                &lt;/div&gt; 
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;                   
                                &lt;div class="question-text"&gt;
                                    &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                                &lt;/div&gt;
                                
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks" style="float:right;"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                                    Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;hr&gt;
                                &lt;div class="options-section"&gt;
                                    ${optionsHTML}
                                &lt;/div&gt;
                                &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;div class="answer-section"&gt;
                                    &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                    &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                            &lt;hr&gt;`;

                        subjectDiv.innerHTML += questionHTML;

                        // Calculate the score based on the user's answers
                        const correctAnswers = questionDetail.correctAnswer.split(';');
                        const userAnswers = userAnswer.split(';');

                        if (isCorrect) {
                            totalScore += parseFloat(questionDetail.correctScore); // Add correct score
                        } else if (userAnswers.length &gt; 0 &amp;&amp; userAnswers.some(answer =&gt; correctAnswers.includes(answer))) {
                            totalScore += parseFloat(questionDetail.correctScore); // If partially correct, count some marks
                        } else {
                            totalScore += parseFloat(questionDetail.incorrectScore); // Deduct negative marks
                        }

                        // Insert the ad after every 3 questions
                        if ((index + 1) % 3 === 0) {
                            const adDiv = document.createElement('div');
                            adDiv.id = 'adModel';
                            adDiv.innerHTML = '&lt;h3&gt;Ad&lt;/h3&gt;&lt;p&gt;Advertisement goes here...&lt;/p&gt;';
                            adDiv.style.border = '1px solid gray';
                            adDiv.style.padding = '10px';
                            adDiv.style.margin = '10px 0';
                            subjectDiv.appendChild(adDiv);
                        }
                    });
                    detailedResultsContainer.appendChild(subjectDiv);
                }
            }

            function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            }

            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/unsymmetrical-bending.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-8238668084631567765</guid><pubDate>Sun, 27 Oct 2024 17:01:00 +0000</pubDate><atom:updated>2025-03-23T15:30:38.110+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Test Series</category><title>Aerodynamics &amp; Fluid Mechanics</title><description>&lt;html lang="en"&gt;
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                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt; 
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                            &lt;p&gt;1. Calculate the lift coefficient (Cl) for a thin airfoil at a 5-degree angle of attack, considering a subsonic flow. Assume 2D flow and ideal conditions. (in 2 decimal)&lt;/p&gt; 
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                                &lt;input id="nat-answer1" name="nat-options" type="text" /&gt; 
                            &lt;/div&gt; 
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Aerospace" data-type="MCQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;2. Which airfoil type has the highest maximum lift coefficient (Clmax) under subsonic conditions?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Symmetric Airfoil&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Flat Plate Airfoil&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options2" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Cambered Airfoil&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Blended Airfoil&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="55.0" data-correct-score="2" data-incorrect-score="0" data-max="54.5" data-min="55.5" data-precision="1" data-subject="Aerospace" data-type="NAT" data-explanation="tan(θ)=2⋅cot(β)/(M^2-1)"&gt; 
                            &lt;div class="question-info"&gt; 
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt; 
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt; 
                            &lt;/div&gt; 
                            &lt;p&gt;3. For a supersonic flow, determine the shock wave angle in degrees when the Mach number is 2.5 and the deflection angle is 15 degrees.(in 1 decimal)&lt;/p&gt; 
                            &lt;div class="options"&gt; 
                                &lt;input id="nat-answer3" name="nat-options" type="text" /&gt; 
                            &lt;/div&gt; 
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="A;B" data-correct-score="2" data-incorrect-score="0" data-question-score="1" data-subject="Aerospace" data-type="MSQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;4. Select the correct properties of a turbulent boundary layer:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options4" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;Higher skin friction drag compared to laminar boundary layer&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options4" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;Greater mixing and momentum transfer&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options4" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;Lower pressure drag compared to laminar boundary layer&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options4" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;More stable and less prone to separation&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="0.0367" data-correct-score="2" data-incorrect-score="0" data-max="0.0400" data-min="0.0300" data-precision="4" data-subject="Aerospace" data-type="NAT" data-explanation="Specific Thrust= (Ve - V0)/g"&gt;
                            &lt;div class="question-info"&gt; 
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt; 
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt; 
                            &lt;/div&gt; 
                            &lt;p&gt;5. Calculate the specific thrust (in kN/kg) of a turbojet engine operating at a Mach number of 0.8 at an altitude of 10 km.assuming temperature at 10km=-50 °C and exhaust velocity around 2160 km/hr. (in 4 decimal)&lt;/p&gt; 
                            &lt;div class="options"&gt; 
                                &lt;input id="nat-answer5" name="nat-options" type="text" /&gt; 
                            &lt;/div&gt; 
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Aerospace" data-type="MCQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;6. Which of the following methods is used to reduce induced drag on an aircraft wing?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options6" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Increasing the aspect ratio&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options6" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Using winglets&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options6" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Reducing the wing loading&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options6" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;All of the above&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="0.63" data-correct-score="1" data-incorrect-score="0" data-max="0.60" data-min="0.70" data-precision="2" data-subject="Aerospace" data-type="NAT" data-explanation="Pr= Cp*μ/k"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;7. Determine the Prandtl number for an airfoil experiencing boundary layer transition from laminar to turbulent flow at an altitude of 15,000 meters. (Assuming at altitude 15,000 meters propertiesof air Dynamic viscosity (μ) is 1.42 x 10^-5 kg/(m·s), Specific heat at constant pressure (C_p) is 1005 J/(kg·K) and Thermal conductivity (k) is 0.0227 W/(m·K))&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer7" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="B;D" data-correct-score="2" data-incorrect-score="0" data-question-score="1" data-subject="Aerospace" data-type="MSQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;8. Which of the following methods can be used to delay boundary layer separation on an airfoil?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options8" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;Increasing the angle of attack&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options8" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;Using boundary layer suction&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options8" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;Decreasing the Reynolds number&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options8" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;Using vortex generators&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="0.001" data-correct-score="2" data-incorrect-score="0" data-max="0.003" data-min="0.001" data-precision="3" data-subject="Aerospace" data-type="NAT" data-explanation="Cd = 1.328/Sqrt(Re)"&gt; 
                            &lt;div class="question-info"&gt; 
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt; 
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt; 
                            &lt;/div&gt; 
                            &lt;p&gt;9. Calculate the drag coefficient (Cd) of a flat plate at zero angle of attack in incompressible flow for a Reynolds number of 1 x 10^6. (in 3 decimal)&lt;/p&gt; 
                            &lt;div class="options"&gt; 
                                &lt;input id="nat-answer9" name="nat-options" type="text" /&gt; 
                            &lt;/div&gt; 
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="A;C" data-correct-score="2" data-incorrect-score="0" data-question-score="1" data-subject="Aerospace" data-type="MSQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;10. Which factors increase the wave drag in a transonic aircraft?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options10" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;Increasing Mach number&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options10" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;Decreasing thickness-to-chord ratio&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options10" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;Increasing wing sweep&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options10" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;Decreasing Mach number&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="0.98" data-correct-score="2" data-incorrect-score="0" data-max="1.00" data-min="0.00" data-precision="2" data-subject="Aerospace" data-type="NAT" data-explanation="M_cr ≈ 1 - 0.2⋅(t/c)"&gt; 
                            &lt;div class="question-info"&gt; 
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt; 
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt; 
                            &lt;/div&gt; 
                            &lt;p&gt;11. Calculate the critical Mach number for an airfoil with a thickness-to-chord ratio of 12%. (in 2 deicmal)&lt;/p&gt; 
                            &lt;div class="options"&gt; 
                                &lt;input id="nat-answer11" name="nat-options" type="text" /&gt; 
                            &lt;/div&gt; 
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Aerospace" data-type="MCQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;12. In compressible flow, the Prandtl-Glauert transformation is used to:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options12" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Estimate wave drag&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options12" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Relate pressure coefficient in compressible and incompressible flows&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options12" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Predict boundary layer separation&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options12" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Determine shock wave strength&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="A;D" data-correct-score="2" data-incorrect-score="0" data-question-score="1" data-subject="Aerospace" data-type="MSQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;13. Select the correct statements regarding supersonic flow over a wedge:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options13" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;The shock wave angle decreases with increasing Mach number&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options13" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;The shock wave is always normal to the flow&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options13" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;The pressure downstream of the shock wave decreases&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options13" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;The flow behind the shock wave is subsonic&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="2.07" data-correct-score="2" data-incorrect-score="0" data-max="2.10" data-min="2.00" data-precision="2" data-subject="Aerospace" data-type="NAT" data-explanation="C_l =L/(q*S)"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Numerical Answer Type&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt;| Negative Marks: &lt;span style="color: red;"&gt;0&lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;14. Calculate the lift coefficient (Cl) for an aircraft with a lift of 50,000 N, a wing area of 40 m², and a dynamic pressure of 600 N/m². (in 2 decimal)&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;input id="nat-answer14" name="nat-options" type="text" /&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-subject="Aerospace" data-type="MCQ" data-explanation=""&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;span class="question-marks"&gt;Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; | Negative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;15. In high-speed flows, the purpose of a converging-diverging nozzle is to:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Decrease velocity in the subsonic region&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options15" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Decrease temperature in the diverging section&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Maintain constant pressure throughout the flow&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Accelerate the flow to supersonic speeds&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;div id="numeric-keypad" style="display: none;"&gt;
                            &lt;div class="options"&gt;
                                &lt;h3&gt;Numeric Keypad&lt;/h3&gt;
                                &lt;div&gt;
                                    &lt;button onclick="addToInput('1')"&gt;1&lt;/button&gt;
                                    &lt;button onclick="addToInput('2')"&gt;2&lt;/button&gt;
                                    &lt;button onclick="addToInput('3')"&gt;3&lt;/button&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;button onclick="addToInput('4')"&gt;4&lt;/button&gt;
                                    &lt;button onclick="addToInput('5')"&gt;5&lt;/button&gt;
                                    &lt;button onclick="addToInput('6')"&gt;6&lt;/button&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;button onclick="addToInput('7')"&gt;7&lt;/button&gt;
                                    &lt;button onclick="addToInput('8')"&gt;8&lt;/button&gt;
                                    &lt;button onclick="addToInput('9')"&gt;9&lt;/button&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;button onclick="addToInput('0')"&gt;0&lt;/button&gt;
                                    &lt;button onclick="addToInput('.')"&gt;.&lt;/button&gt;
                                    &lt;button onclick="toggleSign()"&gt;+/-&lt;/button&gt;                                    
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;button onclick="clearInput()"&gt;C&lt;/button&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;                   
                    &lt;div class="col-md-4" style="padding-bottom: 80px; width: 33.333333%;"&gt;
                        &lt;div id="subject-stats"&gt;
                            &lt;div class="quiz-attempt-inline-block" style="width: 180px;"&gt;
                                &lt;div class="qbtn green-answer" id="answered-count" style="background: #449d44;"&gt;0&lt;/div&gt;
                                Answered  
                            &lt;/div&gt;
                            &lt;div class="quiz-attempt-inline-block" style="width: 180px;"&gt;
                                &lt;div class="qbtn red-unanswer" id="unanswered-count" style="background: #c9302c;"&gt;0&lt;/div&gt;
                                Unanswered  
                            &lt;/div&gt;
                            &lt;div class="quiz-attempt-inline-block" style="width: 180px;"&gt;
                                &lt;div class="qbtn yellow-review" id="review-count" style="background: #ec971f;"&gt;0&lt;/div&gt;
                                Review-Later (RL) 
                            &lt;/div&gt;
                            &lt;div class="quiz-attempt-inline-block" style="width: 180px;"&gt;
                                &lt;div class="qbtn black-not-visited" id="not-visited-count" style="background: #212121; color: white;"&gt;0&lt;/div&gt;
                                Not-visited  
                            &lt;/div&gt;
                            &lt;div style="clear: both;"&gt;&lt;/div&gt;
                        &lt;/div&gt;
                        &lt;div class="question-palette" id="question-palette"&gt;&lt;/div&gt;
                    &lt;/div&gt;                                      
                &lt;/div&gt;
            &lt;/div&gt;
            &lt;div id="footer_buttons"&gt;                   
                &lt;button id="clear"&gt;Clear&lt;/button&gt;
                &lt;button id="mark-for-review"&gt;Mark for Review&lt;/button&gt;
                &lt;button id="prev"&gt;Back&lt;/button&gt;
                &lt;button id="next"&gt;Save &amp;amp; Next&lt;/button&gt;
                &lt;button id="submit"&gt;Submit&lt;/button&gt;
            &lt;/div&gt;
        &lt;/div&gt;

        &lt;div id="calc-container" style="display: none; position: absolute; cursor: move;"&gt;
            &lt;div class="panel window window-thinborder c6 panel-htop" style="width: 480px;"&gt;
                &lt;div class="panel-header panel-header-noborder window-header" id="drag-header" style="width: 478px; cursor: move;"&gt;
                    &lt;div class="panel-icon icon-sum"&gt;&lt;/div&gt;
                    &lt;div class="panel-tool"&gt;
                        &lt;a href="javascript:;" class="panel-tool-collapse"&gt;&lt;/a&gt;
                        &lt;a href="javascript:;" class="panel-tool-close"&gt;&lt;/a&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div id="calc" class="easyui-window panel-body panel-body-noborder window-body"
                    title=""
                    style="width: 478px; height: 300px;"
                    data-options="iconCls:'icon-sum',minimizable:false,maximizable:false,resizable:false,border:'thin',cls:'c6',closed:true"&gt;
                    &lt;!-- Replace the URL with your calculator URL or embed code --&gt;
                    &lt;iframe src="https://shorturl.at/htFOS"
                        width="475px"
                        height="300px"
                        scrolling="no"
                        frameborder="0"&gt;
                    &lt;/iframe&gt;
                &lt;/div&gt;
            &lt;/div&gt;
        &lt;/div&gt;
           
       &lt;div id="result-container" style="display: none;"&gt;    
            &lt;p&gt;Thank you, &lt;b&gt;&lt;span id="user-name-display"&gt;User&lt;/span&gt;&lt;/b&gt; for attempting the Test&lt;/p&gt;
         
         	&lt;div style="display: flex;"&gt;
                &lt;button style="float: right;" onclick="window.location.href='https://aerogatetopper.blogspot.com/p/dashboard.html';"&gt;Quiz Dashboard&lt;/button&gt;
                &lt;button style="float: left;" onclick="https://aerogatetopper.blogspot.com/2024/10/aerodynamics-fluid-mechanics.html';"&gt;Restart Quiz&lt;/button&gt;                
            &lt;/div&gt;
         
         &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"
     crossorigin="anonymous"&gt;&lt;/script&gt;
&lt;ins class="adsbygoogle"
     style="display:block; text-align:center;"
     data-ad-layout="in-article"
     data-ad-format="fluid"
     data-ad-client="ca-pub-2922315402866630"
     data-ad-slot="4993484640"&gt;&lt;/ins&gt;
&lt;script&gt;
     (adsbygoogle = window.adsbygoogle || []).push({});
&lt;/script&gt;
         
            &lt;br /&gt;
            &lt;table&gt;
                &lt;thead&gt;
                    &lt;tr&gt;
                        &lt;th&gt;Subject&lt;/th&gt;
                        &lt;th&gt;Score&lt;/th&gt;
                        &lt;th&gt;Time Spent&lt;/th&gt;
                        &lt;th&gt;Correct&lt;/th&gt;
                        &lt;th&gt;Wrong&lt;/th&gt;
                        &lt;th&gt;Unattempted&lt;/th&gt;
                    &lt;/tr&gt;
                &lt;/thead&gt;
                &lt;tbody id="result-body"&gt;&lt;/tbody&gt;
            &lt;/table&gt;
         &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"
     crossorigin="anonymous"&gt;&lt;/script&gt;
&lt;ins class="adsbygoogle"
     style="display:block; text-align:center;"
     data-ad-layout="in-article"
     data-ad-format="fluid"
     data-ad-client="ca-pub-2922315402866630"
     data-ad-slot="4993484640"&gt;&lt;/ins&gt;
&lt;script&gt;
     (adsbygoogle = window.adsbygoogle || []).push({});
&lt;/script&gt;
         
            &lt;!-- &lt;button id="restart" onclick="restartQuiz()"&gt;Restart Quiz&lt;/button --&gt;
            &lt;canvas height="200" id="timeSpentChart" width="400"&gt;&lt;/canvas&gt;
         &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"
     crossorigin="anonymous"&gt;&lt;/script&gt;
&lt;ins class="adsbygoogle"
     style="display:block; text-align:center;"
     data-ad-layout="in-article"
     data-ad-format="fluid"
     data-ad-client="ca-pub-2922315402866630"
     data-ad-slot="4993484640"&gt;&lt;/ins&gt;
&lt;script&gt;
     (adsbygoogle = window.adsbygoogle || []).push({});
&lt;/script&gt;
            &lt;div id="detailed-results" style="left: 20px;"&gt;&lt;/div&gt;
         &lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"
     crossorigin="anonymous"&gt;&lt;/script&gt;
&lt;ins class="adsbygoogle"
     style="display:block; text-align:center;"
     data-ad-layout="in-article"
     data-ad-format="fluid"
     data-ad-client="ca-pub-2922315402866630"
     data-ad-slot="4993484640"&gt;&lt;/ins&gt;
&lt;script&gt;
     (adsbygoogle = window.adsbygoogle || []).push({});
&lt;/script&gt;
        &lt;/div&gt;
        &lt;script&gt;
            let currentQuestionIndex = 0;
            let questions = [];
            let currentSubject = '';
            let timerInterval; 
            const questionStartTimes = [];
            let timeTakenArray = {};
            let subjectData = {};
            let userName = '';
            let countdownMinutes = 45;
            let countdownSeconds = countdownMinutes * 60;
            let targetTime;
            document.getElementById("registrationForm").addEventListener("submit", function(e) {
              e.preventDefault();
              var formData = new FormData(this);
              userName = formData.get('username');

              // Hide user-info and show start-page immediately
              document.getElementById('user-info').style.display = 'none';
              document.getElementById('start-page').style.display = 'block';

              fetch("https://script.google.com/macros/s/AKfycbyrfDJmI2KwyzUJOY8yCTTpuHIuqSLu2gbGPC0q8Lvqd7GeURM9PjqtKjXXkG9E14dO/exec", {
                  method: "POST",
                  body: formData
              })
              .then(response =&gt; response.json())
              .then(data =&gt; {
                  if (!data.success) {
                      alert("Error: " + data.error);
                      // Optionally show the user-info back if there was an error
                      document.getElementById('user-info').style.display = 'block';
                      document.getElementById('start-page').style.display = 'none';
                  }
              })
              .catch(error =&gt; {
                  console.error("Fetch error:", error);
                  alert("There was an error processing your request.");
                  // Optionally show the user-info back if there was an error
                  document.getElementById('user-info').style.display = 'block';
                  document.getElementById('start-page').style.display = 'none';
              });
          });
            
            document.getElementById('calc-btn').addEventListener('click', function () {
                const calcContainer = document.getElementById('calc-container');
                if (calcContainer.style.display === 'none' || calcContainer.style.display === '') {
                    calcContainer.style.display = 'block';
                } else {
                    calcContainer.style.display = 'none';
                }
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.appendChild(calcContainer);
            });

            const calcContainer = document.getElementById('calc-container');
            let offsetX, offsetY, isDragging = false;
            calcContainer.style.position = 'absolute';

            calcContainer.addEventListener('mousedown', (e) =&gt; {
                isDragging = true;
                offsetX = e.clientX - calcContainer.getBoundingClientRect().left;
                offsetY = e.clientY - calcContainer.getBoundingClientRect().top;
                document.addEventListener('mousemove', moveAt);
            });

            document.addEventListener('mouseup', () =&gt; {
                if (isDragging) {
                    isDragging = false;
                    document.removeEventListener('mousemove', moveAt);
                }
            });

            function moveAt(e) {
                if (isDragging) {
                    const newLeft = e.clientX - offsetX;
                    const newTop = e.clientY - offsetY;
                    calcContainer.style.left = newLeft + 'px';
                    calcContainer.style.top = newTop + 'px';
                }
            }

            function initializeSubjectData() {
                const questionElements = document.querySelectorAll('.question');
                questionElements.forEach((question) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjectData[subject]) {
                        subjectData[subject] = {
                            markedForReview: new Set(),
                            answeredQuestions: new Set(),
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            totalQuestions: 0
                        };
                    }
                    timeTakenArray[subject] = [];
                    subjectData[subject].totalQuestions++;
                });
            }

            document.getElementById('start-button').onclick = function() {
                document.getElementById('start-page').style.display = 'none';
                document.getElementById('fullscreen-container').style.display = 'block';
                startQuiz();
            };

            function startQuiz() {
                initializeSubjectData();
                showSubject('Aerospace');
                questionStartTimes[currentQuestionIndex] = Date.now();
                startCountdown();
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                document.addEventListener('keydown', function(event) {
                    event.preventDefault();
                });
                document.addEventListener('contextmenu', function(e) {
                    e.preventDefault();
                });
                if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
            }

            function showSubject(subject) {
                currentSubject = subject;
                questions = Array.from(document.querySelectorAll(`.question[data-subject="${subject}"]`));
                currentQuestionIndex = 0;
                updateQuestionDisplay();
                updateFooterButtons();
                updateQuestionPalette();
                questionStartTimes[currentQuestionIndex] = Date.now();
            }

            function updateQuestionDisplay() {
                document.querySelectorAll('.question').forEach((question) =&gt; {
                    question.style.display = 'none';
                });
                if (questions.length &gt; 0) {
                    questions[currentQuestionIndex].style.display = 'block';
                    if (questions[currentQuestionIndex].getAttribute('data-type') === 'NAT') {
                        document.getElementById('numeric-keypad').style.display = 'block';
                    } else {
                        document.getElementById('numeric-keypad').style.display = 'none';
                    }
                }
            }

            function updateFooterButtons() {
                document.getElementById('prev').style.display = currentQuestionIndex === 0 ? 'none' : 'inline';
                document.getElementById('next').style.display = currentQuestionIndex === questions.length - 1 ? 'none' : 'inline';
                document.getElementById('footer_buttons').style.display = questions.length &gt; 0 ? 'block' : 'none';
            }

            document.getElementById('prev').onclick = function(){
                if (currentQuestionIndex &gt; 0) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex--;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('next').onclick = function(){
                if (currentQuestionIndex &lt; questions.length - 1) {
                    recordTimeTaken();
                    handleQuestionStateBeforeChange();
                    currentQuestionIndex++;
                    updateQuestionDisplay();
                    updateFooterButtons();
                    updateQuestionPalette();
                    questionStartTimes[currentQuestionIndex] = Date.now();
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                }
            }

            document.getElementById('clear').onclick = function(){
                const currentQuestion = questions[currentQuestionIndex];
                currentQuestion.querySelectorAll('input:checked').forEach(input =&gt; input.checked = false);
                subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();
                
                updateQuestionPalette();
            }

            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestionIndex];
                const timeTaken = (questionEndTime - questionStartTime) / 1000;
                const subject = currentSubject;            
                if (!timeTakenArray[subject]) {
                    timeTakenArray[subject] = {};
                }
                if (!timeTakenArray[subject][currentQuestionIndex]) {
                    timeTakenArray[subject][currentQuestionIndex] = 0;
                }
                timeTakenArray[subject][currentQuestionIndex] += timeTaken;
                questionStartTimes[currentQuestionIndex] = questionEndTime;
            }

            document.getElementById('submit').onclick = function(){
                recordTimeTaken();
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';    
                document.getElementById('confirmSubmit').onclick = function() {
                    document.getElementById('fullscreen-container').style.display = 'none';
                    document.getElementById('question-palette').style.display = 'none';
                    modal.style.display = 'none';    
                    const adModal = document.getElementById('adModal');
                    const adCloseButton = document.getElementById('adClose');
                    adModal.style.display = 'block';    
                    setTimeout(() =&gt; {
                        adCloseButton.style.display = 'inline';
                    }, 5000);    
                    adCloseButton.onclick = function() {
                        adModal.style.display = 'none';
                        displayResults(); // Ensure this function is called to show results
                    };    
                    setTimeout(() =&gt; {
                        if (adModal.style.display !== 'none') {
                            adModal.style.display = 'none';
                            document.getElementById('result-container').style.display = 'block'; // Show result container
                            showResult(); // Ensure this function is called to show results
                        }
                    }, 10000);    
                    clearInterval(timerInterval);
                };    
                document.getElementById('cancelSubmit').onclick = function() {
                    modal.style.display = 'none';
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();
                  if (window.matchMedia("(orientation: portrait)").matches) {
                    screen.orientation.lock("landscape").catch(function(error) {
                        console.error("Orientation lock failed: ", error);
                    });
                }
                };    
                const exitFullScreen = document.exitFullscreen || document.mozCancelFullScreen || document.webkitExitFullscreen || document.msExitFullscreen;
                if (exitFullScreen) exitFullScreen.call(document);
            }

            function displayResults() {
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('user-name-display').innerText = userName;
                showResult();
                // window.location.href = './results.html'; 
            }

            document.getElementById('mark-for-review').onclick = function()  {
                const subjectMarks = subjectData[currentSubject].markedForReview;
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                if (subjectMarks.has(currentQuestionIndex)) {
                    subjectMarks.delete(currentQuestionIndex);
                } else {
                    subjectMarks.add(currentQuestionIndex);
                }
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }
                updateQuestionPalette();
            }

            function handleQuestionStateBeforeChange() {
                const currentQuestion = questions[currentQuestionIndex];
                const userAnswer = getUserAnswer(currentQuestion);

                // Save the user's answer
                if (userAnswer) {
                    subjectData[currentSubject].answeredQuestions.add(currentQuestionIndex);
                } else {
                    subjectData[currentSubject].answeredQuestions.delete(currentQuestionIndex);
                }

                // Always mark the question as seen
                markAsSeen(currentQuestionIndex);
            }

            function updateQuestionStats() {
                // Count answered questions (green buttons)
                const answeredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'green').length;

                // Count marked for review questions (orange buttons)
                const markedForReviewCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'orange').length;

                // Total questions in the current subject
                const totalQuestions = questions.length;

                // Count unanswered questions (red buttons)
                const unansweredCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'red').length;

                // Count not visited questions (black buttons)
                const notVisitedCount = Array.from(document.querySelectorAll('#question-palette button'))
                    .filter(button =&gt; button.style.backgroundColor === 'black').length;

                // Update the counts in the HTML
                document.getElementById('answered-count').textContent = `${answeredCount}`;
                document.getElementById('unanswered-count').textContent = `${unansweredCount}`; // Use the correct count
                document.getElementById('review-count').textContent = `${markedForReviewCount}`;
                document.getElementById('not-visited-count').textContent = `${notVisitedCount}`;
            }

            function updateQuestionPalette() {
                const palette = document.getElementById('question-palette');
                palette.innerHTML = '';
                palette.appendChild(document.createElement('br'));
                palette.appendChild(document.createElement('hr'));
                const subjectHeading = document.createElement('h3');
                subjectHeading.textContent = `${currentSubject} Questions`;  
                palette.appendChild(subjectHeading);
                palette.appendChild(document.createElement('hr'));

                questions.forEach((question, index) =&gt; {
                    const button = document.createElement('button');
                    button.textContent = index + 1;
                    button.classList.toggle('active', index === currentQuestionIndex);
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();

                    const subjectMarks = subjectData[currentSubject].markedForReview;
                    const subjectAnswered = subjectData[currentSubject].answeredQuestions;

                    // Set button background color based on question state
                    if (subjectAnswered.has(index)) {
                        button.style.backgroundColor = 'green'; // Answered
                    } else if (subjectMarks.has(index)) {
                        button.style.backgroundColor = 'orange'; // Marked for Review
                    } else if (questions[index].seen) {
                        button.style.backgroundColor = 'red'; // Unanswered
                    } else {
                        button.style.backgroundColor = 'black'; // Not Visited
                    }

                    // Add event handler for question button
                    button.onclick = () =&gt; {
                        recordTimeTaken();
                        handleQuestionStateBeforeChange();
                        currentQuestionIndex = index;
                        updateQuestionDisplay();
                        updateFooterButtons();
                        updateQuestionPalette();
                        questionStartTimes[currentQuestionIndex] = Date.now();
                        updateQuestionStats(); // Update stats when changing questions
                    };
                    palette.appendChild(button);
                });

                updateQuestionStats(); // Update stats when rendering the palette
            }

            function markAsSeen(questionIndex) {
                questions[questionIndex].seen = true;
            }

            function startCountdown() {
                targetTime = Date.now() + countdownSeconds * 1000;
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        submitQuiz();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }    

            function updateTimerDisplay() {
                const remainingTime = targetTime - Date.now();
                const minutes = Math.floor(remainingTime / 60000);
                const seconds = Math.floor((remainingTime % 60000) / 1000);
                document.getElementById('timer').textContent = `${minutes}m ${seconds}s`;
                if (remainingTime &lt; 600000) {
                  document.getElementById('timer').style.color = 'red';
                } else {
                  document.getElementById('timer').style.color = '';
                }
            }
          
          

            function validateUserAnswer(userAnswer, correctAnswer, precision, min, max) {
                const userAnswerNum = parseFloat(userAnswer);
                const userDecimals = (userAnswer.split('.')[1] || '').length;
                const isInRange = userAnswerNum &gt;= min &amp;&amp; userAnswerNum &lt;= max;
                
                // Check if the answer has the correct number of decimal places
                const isCorrectPrecision = userDecimals === precision;

                return isInRange &amp;&amp; isCorrectPrecision;
            }

            function getUserAnswer(question) {
                const radioChecked = Array.from(question.querySelectorAll('input[type="radio"]:checked')).map(input =&gt; input.value);
                const checkboxChecked = Array.from(question.querySelectorAll('input[type="checkbox"]:checked')).map(input =&gt; input.value);
                const textInput = Array.from(question.querySelectorAll('input[type="text"]')).map(input =&gt; input.value.trim());
                return [...radioChecked, ...checkboxChecked, ...textInput.filter(value =&gt; value !== '')].sort().join(';');
            }

            function addToInput(value) {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value += value; // Append the value to the current input field
                }
            }

            function clearInput() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    inputField.value = ''; // Clear the current input field
                }
            }

            function toggleSign() {
                // Get the current question's input field
                const inputField = questions[currentQuestionIndex].querySelector('input[type="text"]');
                if (inputField) {
                    if (inputField.value.startsWith('-')) {
                        inputField.value = inputField.value.substring(1); // Remove the negative sign
                    } else {
                        inputField.value = '-' + inputField.value; // Add the negative sign
                    }
                }
            }

            document.getElementById('restart').addEventListener('click', function() {
                // Reset quiz state
                currentQuestionIndex = 0;
                subjectData = {};
                timeTakenArray = {};

                // Show quiz
                document.getElementById('question-palette').style.display = 'block'; 

                // Call the function to start the quiz
                startQuiz(); 
            });

            function showResult() {
                const subjects = {};
                let totalScore = 0;
                const questions = document.querySelectorAll('.question');

                questions.forEach((question, i) =&gt; {
                    const subject = question.getAttribute('data-subject');
                    if (!subjects[subject]) {
                        subjects[subject] = {
                            correct: 0,
                            wrong: 0,
                            unattempted: 0,
                            score: 0,
                            timeSpent: 0,
                            questions: []
                        };
                    }

                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');
                    const userAnswer = getUserAnswer(question);
                  	const explanation = question.getAttribute('data-explanation') || "No explanation available.";

                    const optionElements = question.querySelectorAll('.options div label');
                    const options = Array.from(optionElements).map(label =&gt; label.innerHTML.trim());
                  	

                    let questionDetail = {
                        questionText: question.querySelector('p').innerHTML,
                        userAnswer: userAnswer || 'Not answered',
                        correctAnswer: correctAnswer,
                        result: 'Wrong',
                        type: questionType,
                        correctScore: parseFloat(question.getAttribute('data-correct-score')) || 1,
                        incorrectScore: parseFloat(question.getAttribute('data-incorrect-score')) || -0.33,
                        options: options,
                        question: question,
                      	explanation: explanation
                      
                    };
                    evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjects[subject]);

                    subjects[subject].questions.push(questionDetail);
                    const timeSpent = timeTakenArray[subject][i] || 0;
                    subjects[subject].timeSpent += parseFloat(timeSpent);
                });
                displayDetailedResults(subjects);
                displayDetailed(subjects);
                renderTimeSpentChart(subjects);
                checkUserPerformance(subjects);
            }

            function checkUserPerformance(subjects) {
                let totalScore = 0;
                let totalQuestions = 0;

                for (const subject in subjects) {
                    totalScore += subjects[subject].score;
                    totalQuestions += subjects[subject].questions.length;
                }

                const percentage = (totalScore / (totalQuestions * 1)) * 100;

                let message = '';
                if (percentage &gt; 60) {
                    message = `&#127881;&#127880; Congratulations, ${userName}! You are a Ranker! &#127880;&#127881;`;
                    showWinnerAnimation(message);
                } else if (percentage &gt;= 30) {
                    message = `&#127881; Congratulations , ${userName}. You have clear the cutoff. Practice more! &#127881;`;
                    showFeedbackMessage(message);
                } else {
                    message = `&#128557;&#128557; Sorry, ${userName}. You need to work harder!`;
                    showFeedbackMessage(message);
                }
            }

            function showWinnerAnimation(message) {
                const winnerMessage = document.createElement('div');
                winnerMessage.innerHTML = `&lt;h1 style="color: green;"&gt;${message}&lt;/h1&gt;`;
                winnerMessage.style.position = 'fixed';
                winnerMessage.style.top = '50%';
                winnerMessage.style.left = '50%';
                winnerMessage.style.transform = 'translate(-50%, -50%)';
                winnerMessage.style.zIndex = '1000';
                winnerMessage.style.fontSize = '2em';
                winnerMessage.style.textAlign = 'center';
                document.body.appendChild(winnerMessage);

                // Animation effect
                winnerMessage.animate([
                    { transform: 'scale(1)', opacity: 1 },
                    { transform: 'scale(1.1)', opacity: 1 },
                    { transform: 'scale(1)', opacity: 1 }
                ], {
                    duration: 1000,
                    iterations: 3
                });

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(winnerMessage);
                }, 10000);
            }

            function showFeedbackMessage(message) {
                const feedbackMessage = document.createElement('div');
                feedbackMessage.innerHTML = `&lt;h1 style="color: red;"&gt;${message}&lt;/h1&gt;`;
                feedbackMessage.style.position = 'fixed';
                feedbackMessage.style.top = '50%';
                feedbackMessage.style.left = '50%';
                feedbackMessage.style.transform = 'translate(-50%, -50%)';
                feedbackMessage.style.zIndex = '1000';
                feedbackMessage.style.fontSize = '2em';
                feedbackMessage.style.textAlign = 'center';
                document.body.appendChild(feedbackMessage);

                // Remove the message after a few seconds
                setTimeout(() =&gt; {
                    document.body.removeChild(feedbackMessage);
                }, 5000);
            }

            function evaluateAnswer(questionDetail, userAnswer, correctAnswer, questionType, subjectStats) {
                if (questionType === 'NAT') {
                    const dataMin = parseFloat(questionDetail.question.getAttribute('data-min')) || null;
                    const dataMax = parseFloat(questionDetail.question.getAttribute('data-max')) || null;
                    const precision = parseInt(questionDetail.question.getAttribute('data-precision')) || 0;

                    if (validateUserAnswer(userAnswer, correctAnswer, precision, dataMin, dataMax)) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }

                    // Set the correct answer to be the range between dataMin and dataMax
                    questionDetail.correctAnswer = `${dataMin} - ${dataMax}`;
                } else if (questionType === 'MCQ') {
                    if (userAnswer === correctAnswer) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                } else if (questionType === 'MSQ') {
                    const correctAnswers = correctAnswer.split(';').sort().join(';');
                    const userAnswers = userAnswer.split(';').sort().join(';');

                    if (userAnswers === correctAnswers) {
                        questionDetail.result = 'Correct';
                        subjectStats.correct++;
                        subjectStats.score += questionDetail.correctScore;
                    } else if (!userAnswer) {
                        questionDetail.result = 'Unattempted';
                        subjectStats.unattempted++;
                    } else {
                        questionDetail.result = 'Wrong';
                        subjectStats.wrong++;
                        subjectStats.score += questionDetail.incorrectScore;
                    }
                    questionDetail.correctAnswer = correctAnswers.replace(';', ', ');
                }
            }
   
            function displayDetailed(subjects) { 
    const detailedResultsContainer = document.getElementById('detailed-results');
    detailedResultsContainer.innerHTML = ''; // Clear previous results

    for (const subject in subjects) {
        const subjectReport = subjects[subject];
        const subjectDiv = document.createElement('div');
        subjectDiv.innerHTML = `&lt;h3&gt;${subject}&lt;/h3&gt;&lt;ul&gt;`; // Add subject heading

        let totalScore = 0; // Initialize total score

        subjectReport.questions.forEach((questionDetail, index) =&gt; {
            const userAnswer = questionDetail.userAnswer;
            const questionType = questionDetail.type; // Ensure question type is captured properly
            const isCorrect = questionDetail.result === 'Correct';
            const resultSymbol = isCorrect ? '✅' : userAnswer === 'Not answered' ? '❓' : '❌';
            const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === 'Not answered' ? 'not-answered' : 'wrong-answer';

            let correctAnswer = questionDetail.correctAnswer; // Default correct answer
            let optionsHTML = '';

            // Handle each question type properly
            if (questionType === 'MCQ') {
                optionsHTML = '&lt;div&gt;';
                questionDetail.options.forEach((option) =&gt; {
                    const isChecked = userAnswer === option ? 'checked' : '';
                    optionsHTML += 
                        `&lt;div&gt;
                            &lt;label&gt;
                                &lt;input type="radio" disabled ${isChecked}&gt; ${option}
                            &lt;/label&gt;
                        &lt;/div&gt;`;
                });
                optionsHTML += '&lt;/div&gt;';
            } else if (questionType === 'MSQ') {
                optionsHTML = '&lt;div&gt;';
                questionDetail.options.forEach((option) =&gt; {
                    const isChecked = userAnswer.includes(option) ? 'checked' : '';
                    optionsHTML += 
                        `&lt;div&gt;
                            &lt;label&gt;
                                &lt;input type="checkbox" disabled ${isChecked}&gt; ${option}
                            &lt;/label&gt;
                        &lt;/div&gt;`;
                });
                optionsHTML += '&lt;/div&gt;';
            } else if (questionType === 'NAT') {
                optionsHTML = `&lt;strong&gt;Your Input:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;`;
            }

            // Create HTML for question details
            const questionHTML = 
                `&lt;div class="question-result ${backgroundClass}"&gt;
                    &lt;div class="question-meta"&gt;
                        &lt;strong&gt;Question Type:&lt;/strong&gt; ${questionType || 'Unknown'}&lt;br&gt;                    
                    &lt;/div&gt; 
                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;                 
                    &lt;div class="question-text"&gt;
                        &lt;strong&gt;Question ${index + 1}):&lt;/strong&gt; ${questionDetail.questionText}
                    &lt;/div&gt;
                    
                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                    &lt;span class="question-marks" style="float:right;"&gt;
                        Marks for correct answer: &lt;span style="color: green"&gt;${questionDetail.correctScore}&lt;/span&gt; | 
                        Negative Marks: &lt;span style="color: red"&gt;${Math.abs(questionDetail.incorrectScore)}&lt;/span&gt;
                    &lt;/span&gt;
                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                    &lt;div class="options-section"&gt;
                        ${optionsHTML}
                    &lt;/div&gt;
                    &lt;div class="angled-text"&gt;AERO GATE TOPPER&lt;/div&gt;
                    &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                    &lt;div class="answer-section"&gt;
                        &lt;strong&gt;Your Answer:&lt;/strong&gt; ${userAnswer || 'Not answered'}&lt;br&gt;
                        &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                        &lt;strong&gt;Correct Answer:&lt;/strong&gt; ${correctAnswer}&lt;br&gt;
                        &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                        &lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${questionDetail.result}&lt;br&gt;
                        &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                        &lt;strong&gt;Explanation:&lt;/strong&gt; ${questionDetail.explanation}&lt;br&gt;&lt;div&gt;&lt;br&gt;&lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;hr&gt;`;

            subjectDiv.innerHTML += questionHTML;

            // Insert the Google Ad after every 3 questions
             if ((index + 1) % 3 === 0) {
                const adDiv = document.createElement('div');
                adDiv.className = 'ads-container';
                adDiv.innerHTML = `
                    &lt;ins class="adsbygoogle"
                        style="display:block; text-align:center;"
                        data-ad-client="ca-pub-2922315402866630"
                        data-ad-slot="4993484640"
                        data-ad-format="auto"&gt;&lt;/ins&gt;
                `;
                subjectDiv.appendChild(adDiv);

                // Dynamically load Google Ads script
                setTimeout(() =&gt; {
                    if (window.adsbygoogle) {
                        window.adsbygoogle.push({});
                    }
                }, 500);
            }
        });
        detailedResultsContainer.appendChild(subjectDiv);
    }
}


            function displayDetailedResults(subjects) {
                const resultBody = document.getElementById('result-body');
                resultBody.innerHTML = '';
                let totalScore = 0;
                let totalCorrect = 0;
                let totalWrong = 0;
                let totalUnattempted = 0;
                let totalTimeSpent = 0;

                for (const subject in subjects) {
                    const subjectResult = subjects[subject];
                    totalScore += subjectResult.score;
                    totalCorrect += subjectResult.correct;
                    totalWrong += subjectResult.wrong;
                    totalUnattempted += subjectResult.unattempted;
                    totalTimeSpent += subjectResult.timeSpent;

                    // Subject summary row
                    const subjectRow = `
                        &lt;tr class="category-row"&gt;
                            &lt;td style="font-weight: bold;"&gt;${subject}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.score.toFixed(2)}&lt;/td&gt;
                            &lt;td&gt;${(subjectResult.timeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                            &lt;td&gt;${subjectResult.correct}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.wrong}&lt;/td&gt;
                            &lt;td&gt;${subjectResult.unattempted}&lt;/td&gt;
                        &lt;/tr&gt;
                    `;
                    resultBody.innerHTML += subjectRow;
                }

                // Total summary row
                const totalRow = `
                    &lt;tr class="total-row"&gt;
                        &lt;td style="font-weight: bold;"&gt;Total&lt;/td&gt;
                        &lt;td&gt;${totalScore.toFixed(2)}&lt;/td&gt;
                        &lt;td&gt;${(totalTimeSpent / 60).toFixed(2)} mins&lt;/td&gt;
                        &lt;td&gt;${totalCorrect}&lt;/td&gt;
                        &lt;td&gt;${totalWrong}&lt;/td&gt;
                        &lt;td&gt;${totalUnattempted}&lt;/td&gt;
                    &lt;/tr&gt;
                `;
                resultBody.innerHTML += totalRow;
            }

            function renderTimeSpentChart(subjects) {
                const labels = [];
                const data = [];
                
                // Collect data for the chart
                for (const subject in subjects) {
                    subjects[subject].questions.forEach((questionDetail, index) =&gt; {
                        const timeSpent = timeTakenArray[subject][index] || 0;
                        labels.push(`${subject} - Q${index + 1} (${questionDetail.result})`); // Format label as "SubjectName - Q1"
                        data.push(timeSpent);
                    });
                }

                const ctx = document.getElementById('timeSpentChart').getContext('2d');
                const timeSpentChart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: labels,
                        datasets: [{
                            label: 'Time Spent (seconds)',
                            data: data,
                            backgroundColor: 'rgba(75, 192, 192, 0.2)',
                            borderColor: 'rgba(75, 192, 192, 1)',
                            borderWidth: 1
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true
                            }
                        }
                    }
                });
            }

            // Add event listeners for buttons            
            document.getElementById('start-button').onclick = startQuiz;
            document.getElementById('prev').onclick = prevQuestion;
            document.getElementById('next').onclick = nextQuestion;
            document.getElementById('clear').onclick = clearResponse;
            document.getElementById('submit').onclick = submitQuiz;
            document.getElementById('mark-for-review').onclick = markForReview;
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;


</description><link>https://aerogatetopper.blogspot.com/2024/10/aerodynamics-fluid-mechanics.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEh30sIuQnacrJT7gkNT3XGE3vlzPu5f6BCxgdm5Ms1u48MtDinqkxYmlrwOGz8fjW6jbt1at1vXtD48ufH1wifuAVubLkM7wzrdWdoRS7kaGUltIwyVeXZN3-iUYerXYq14fsxx6dEBeezPMFnBCPrPfvdT2ZZaLtx5eNRH8BWQa6Bf_6IY41lJv28CqeZi=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-7929699351578555086</guid><pubDate>Sun, 07 Jan 2024 03:00:00 +0000</pubDate><atom:updated>2024-01-07T08:30:00.129+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Mock Test</category><title>GATE AEROSPACE PRACTICE MOCK TEST-1</title><description>&lt;!DOCTYPE html&gt;
&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Online Quiz&lt;/title&gt;
        &lt;meta charset="UTF-8"&gt;
        &lt;meta name="viewport" content="width=device-width, initial-scale=1.0"&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        &lt;script src="https://cdnjs.cloudflare.com/ajax/libs/Chart.js/3.7.0/chart.min.js"&gt;&lt;/script&gt;
        &lt;script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"&gt;&lt;/script&gt;

        &lt;script&gt;
       
            let quizStarted = false; // Variable to track if the quiz has started
            let resultDisplayed = false; // Variable to track if the result is displayed
        
            // Function to display a confirmation message when the user tries to leave the page
            window.onbeforeunload = function (e) {
                if (quizStarted || resultDisplayed) {
                    e.preventDefault();
                    e.returnValue = "Data will be lost if you leave the page, are you sure?";
                }
            };
        
            // Function to set quizStarted variable to true when the quiz starts
            function startQuiz() {
                quizStarted = true;
              
                // Enter fullscreen for the quiz container
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

            }   
        
            // Function to set resultDisplayed variable to true when the result is displayed
            function displayResult() {
                resultDisplayed = true;
            }
        &lt;/script&gt;

        &lt;style&gt;
            
            body {
                font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
                margin: 0;
                padding: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #333;
                background-color: #f2f2f2;
            }

            #cont {
                overflow: auto;
                height: 100vh;
                background-color: #fff;
                flex-wrap: wrap;
                flex-direction: row;
            }

            #container {
                background-color: #fff;
                box-shadow: 0 10px 30px rgba(0, 0, 0, 0.96);
                border-radius: 5px;
                height: 100vh;
                width: 100%;
            }

            #quiz-container {
                overflow: auto;
                padding-left: 10px;
                width: 70%;
                height: 90vh;
                background-color: #fff;
            }

            .question {
                margin-top: 10px;
                padding: 10px;
                overflow-y: auto;
                display: none;
                margin-bottom: 20px;
            }

            h1 {
                font-size: 20px;
                margin-top: 20px;
                color: #333;
            }

            p {
                font-size: 16px;
                margin-top: 20px;
                color: #333;
            }

            .options {
                display: flex;
                flex-direction: column;
                flex-wrap: wrap;
                gap: 10px;
            }

            .options div {
                display: flex;
                align-items: center;
            }

            label {
                margin-left: 5px;
                font-size: 14px;
                color: #333;
            }

            input[type="text"],
            input[type="radio"],
            input[type="checkbox"] {
                padding: 8px;
                margin-bottom: 10px;
                border: 1px solid #ccc;
                border-radius: 3px;
            }

            input[type="text"]:focus,
            input[type="radio"]:focus,
            input[type="checkbox"]:focus {
                outline: none;
                border-color: #007bff;
            }

            button {
                display: inline-block;
                padding: 6px 12px;
                margin-left: 0;
                font-size: 14px;
                line-height: 1.42857143;
                text-align: center;
                vertical-align: middle;
                touch-action: manipulation;
                color: #fff;
                border: 1px solid transparent;
                border-radius: 4px;
                user-select: none;
                cursor: pointer;
                background-color: #007bff;
                transition: background-color 0.3s ease;
            }

            button:hover {
                background-color: #0056b3;
            }

            #result {
                text-align: center;
                font-size: 20px;
                font-weight: bold;
                margin-top: 20px;
            }

            #prev,
            #next,
            #submit {
                padding: 10px 20px;
                margin-left: 0;
                border: none;
                border-radius: 4px;
                cursor: pointer;
                transition: background-color 0.3s ease;
            }

            #prev {
                background-color: #f0ad4e;
                border-color: #eea236;
                visibility: visible;
            }

            #next {
                background-color: #5cb85c;
                border-color: #4cae4c;
                visibility: visible;
            }

            #submit {
                background-color: #d9534f;
                border-color: #d43f3a;
            }

            #prev:hover {
                background-color: #eea236;
            }

            #next:hover {
                background-color: #4cae4c;
            }

            #submit:hover {
                background-color: #d43f3a;
            }

            #progress {
                font-size: 1rem;
                margin-top: 10px;
            }

            #report-container {
                display: none;
                margin-top: 20px;
                border: 1px solid #ccc;
                padding: 10px;
                background-color: #f9f9f9;
            }

            .question-report {
                margin: 20px 0;
                width: 100%;
                border: 1px solid #ccc;
                padding: 10px;
                background-color: #fff;
            }

            .correct-answer {
                background-color: #71ba5d;
                color: white;
            }

            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
            }

            .not-answered {
                background-color: #fff;
                color: black;
            }

            #chart-container {
                margin-top: 20px;
                width: 100%;
                max-width: 600px;
            }

            @media screen and (max-width: 600px) {
                p {
                    font-size: 15px;
                }

                label {
                    font-size: 14px;
                }

                input[type="text"],
                input[type="radio"],
                input[type="checkbox"] {
                    width: 20px;
                }
            }

            #question-index-container {
                float: left;
                position: fixed;
                right: 0;
                top: 0;
                height: 100%;
                overflow-y: auto;
                background-color: #f1f1f1;
                padding: 20px;
                box-shadow: -5px 0 5px -5px #333;
            }

            #question-index-list {
                list-style-type: none;
                padding: 0;
                display: flex;
                flex-wrap: wrap;
            }

            #question-index-list li {
                cursor: pointer;
                text-align: center;
                color: #0a0000;
                width: 40px;
                margin: 5px;
                padding: 5px;
                background-color: #fff;
                border-radius: 3px;
                transition: background-color 0.2s;
            }

            #question-index-list li:hover {
                background-color: #d0d0d0;
            }

            .brand-tag {
                position: absolute;
                top: 50%;
                left: 50%;
                transform: translate(-50%, -50%);
                opacity: 4.5;
                font-size: 20px;
                rotate: -30deg;
                color: #0e0c0c;
            }

            @media print {
                .no-print,
                .no-print * {
                    display: none !important;
                }

                body {
                    display: none !important;
                    visibility: hidden !important;
                }
            }

            .modal {
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
                margin: 40px;
                top: 0;
                width: 100%;
                height: 100%;
                overflow: hidden;
                background-color: rgba(0, 0, 0, 0.4);
            }

            .modal-content {
                position: fixed;
                top: 10px;
                left: 50%;
                transform: translate(-50%, -50%);
                background-color: #fefefe;
                margin: 15% auto;
                padding: 20px;
                border: 1px solid #888;
                width: 80%;
                max-width: 400px;
                height: 150px;
                text-align: center;
                border-radius: 5px;
                box-shadow: 0 4px 8px 0 rgba(0, 0, 0, 0.2);
            }

            #confirmSubmit,
            #cancelSubmit {
                padding: 10px 20px;
                margin: 10px;
                cursor: pointer;
                border-radius: 5px;
            }

            #confirmSubmit {
                background-color: #5bc0de;
                border-color: #46b8da;
                color: white;
                border: none;
            }

            #confirmSubmit:hover {
                background-color: #3fb5da;
            }

            #cancelSubmit {
                background-color: #d9534f;
                border-color: #d43f3a;
                color: white;
                border: none;
            }

            #cancelSubmit:hover {
                background-color: #d43f3a;
            }

            #start-page {
                overflow: auto;
                height: 600px;
                margin-left: 30px;
                margin-bottom: 30px;
                padding: 20px;
                background-color: #fff;
                box-shadow: 0 10px 30px rgba(0 0 0 / 96%);
                border-radius: 5px;
            }

            #start-page h1 {
                font-size: 24px;
                color: #333;
            }

            #start-button {
                display: inline-block;
                padding: 12px 24px;
                font-size: 18px;
                background-color: #007bff;
                color: #fff;
                border: none;
                border-radius: 4px;
                cursor: pointer;
            }

            #start-button:hover {
                background-color: #0056b3;
            }

            #score-summary {
                width: 95%;
                border-collapse: collapse;
                margin-top: 20px;
                margin-bottom: 20px;
            }

            #score-summary th {
                background-color: #f2f2f2;
                padding: 10px;
                text-align: center;
            }

            #score-summary td {
                padding: 10px;
                text-align: center;
            }

            #score-summary tbody tr:nth-child(odd) {
                background-color: #f9f9f9;
            }

            #score-summary tbody tr:hover {
                background-color: #e0e0e0;
            }

            #user-score,
            #total-time-taken,
            #correct-answers,
            #wrong-answers,
            #unattempted {
                font-weight: bold;
                color: #007bff;
            }

            #user-score:empty::before,
            #total-time-taken:empty::before,
            #correct-answers:empty::before,
            #wrong-answers:empty::before,
            #unattempted:empty::before {
                content: "Calculating...";
                color: #888;
            }

            #calc-container {
                position: absolute;
                top: 20%;
                left: 70%;
                transform: translate(-50%, -50%);
            }

            #warning-popup {
                position: fixed;
                top: 50%;
                left: 50%;
                transform: translate(-50%, -50%);
                background-color: #fff;
                border: 1px solid #ccc;
                box-shadow: 0px 0px 10px rgba(0, 0, 0, 0.5);
                padding: 20px;
                z-index: 9999;
                text-align: center;
                display: none;
            }

            #warning-popup p {
                margin: 0;
            }

            #warning-popup button {
                margin: 10px;
                padding: 5px 15px;
                background-color: #337ab7;
                color: #fff;
                border: none;
                cursor: pointer;
            }

            button,
            #confirmSubmit,
            #cancelSubmit {
                margin: 5px;
                padding: 5px 15px;
                cursor: pointer;
            }

            .numeric-keyboard {
                flex-wrap: wrap;
            }

            .numeric-keyboard button {
                margin: 5px;
                font-size: 14px;
                cursor: pointer;
            }

            table {
                width: 150px;
            }

            table td {
                text-align: center;
                vertical-align: middle;
                font-weight: bold;
            }
            table button {
                color: #0a0000;
                background-color: #bec9cd;
            }
        &lt;/style&gt;

    &lt;/head&gt;
    &lt;body&gt;
        &lt;!-- Start Page --&gt;
        &lt;div id="start-page"&gt;
            &lt;center&gt;&lt;h2&gt;AERO GATE TOPPER&lt;/h2&gt;&lt;/center&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt; General Instructions:&lt;/u&gt;&lt;/p&gt;
            &lt;p&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;
                &lt;li&gt;The total duration of the examination is 180 minutes (3 hours).&lt;/li&gt;
                &lt;li&gt;The clock will be set on the server. The countdown timer in the top right corner of the screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.&lt;/li&gt;
                &lt;li&gt;To answer a question, do the following:&lt;/li&gt;
            &lt;/ol&gt;
            &lt;p style="font-weight: bold;"&gt;&lt;u&gt;Navigating to a Question:&lt;/u&gt;&lt;/p&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;To answer a question, do the following:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;Click on the question number in the Question Palette to go to that question directly.&lt;/li&gt;&lt;li&gt;Select an answer for a multiple-choice type question. Use the virtual numeric keypad to enter a number as the answer for a numerical-type question.&lt;/li&gt;&lt;li&gt;Click on &lt;b&gt;Save and Next&lt;/b&gt; to save your answer for the current question and then go to the next question.&lt;/li&gt;&lt;li&gt;&lt;span style="font-weight: 700;"&gt;&lt;span style="color: red;"&gt;Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on its question number.&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;               
            &lt;li&gt;
            You can view all the questions by clicking the Question Paper button. Note that the options for multiple-choice type questions will not be shown.&lt;/li&gt;&lt;/ol&gt;&lt;u style="font-weight: 700;"&gt;Answering a Question:&lt;/u&gt;&lt;br /&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;Procedure for answering a multiple choice type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To select your answer, click on the button on one of the options&lt;/li&gt;&lt;li&gt;To deselect your chosen answer, click on the button of the chosen option again&lt;/li&gt;&lt;li&gt;To change your chosen answer, click on the button of another option&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next &lt;/b&gt;button&lt;/li&gt;&lt;/ol&gt;&lt;li&gt;
            Procedure for answering a numerical answer type question:&lt;/li&gt;
                &lt;ol type="a"&gt;&lt;li&gt;To enter a number as your answer, use the virtual numerical keypad&lt;/li&gt;&lt;li&gt;A fraction (eg.,-0.3 or -.3) can be entered as an answer with or without ‘0’ before the decimal point&lt;/li&gt;&lt;li&gt;To clear your answer, click on the &lt;b&gt;Clear&lt;/b&gt; button&lt;/li&gt;&lt;li&gt;To save your answer, you MUST click on the &lt;b&gt;Save and Next&lt;/b&gt; button&lt;/li&gt;&lt;/ol&gt;  
            &lt;li&gt;
            To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.&lt;/li&gt;&lt;/ol&gt;&lt;ol style="text-align: left;"&gt;
            &lt;/ol&gt;
            &lt;span style="font-weight: 700;"&gt;&lt;u&gt;Paper specific instructions:&lt;/u&gt;&lt;/span&gt;
            &lt;ol style="text-align: left;"&gt;&lt;li&gt;There are a total of 65 questions carrying 100 marks. Questions are of multiple choice type or numerical answer type. A multiple-choice type question will have four choices for the answer with only one correct choice. The answer is a number for numerical answer-type questions,&amp;nbsp;and no choices will be given. A number as the answer should be entered using the virtual keyboard on the monitor.&lt;/li&gt;
                &lt;li&gt;Questions Q.1 – Q.10 belong to the General Aptitude (GA) section and carry a total of 15 marks. Questions Q.1 – Q.5 carry 1 mark each, and questions Q.6 – Q.10 carry 2 marks each.&lt;/li&gt;
                &lt;li&gt;Questions Q. 11 – Q.35 carry 1 mark each. Questions Q.36 – Q.65 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated.&lt;/li&gt;
                &lt;li&gt;Questions not attempted will result in zero marks. Wrong answers for multiple choice type questions will result in NEGATIVE marks. For all 1 mark questions, 1⁄3 mark will be deducted for each wrong answer. For all 2 marks questions, 2⁄3 mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for the wrong answer to the first question and no negative marks for the wrong answer to the second question. There is no negative marking for questions of numerical answer type.&lt;/li&gt;
                &lt;li&gt;A calculator is allowed. Charts, graph sheets, or tables are NOT allowed in the examination hall.&lt;/li&gt;
                &lt;li&gt;Do the rough work in the Scribble Pad provided.&lt;/li&gt;
            &lt;/ol&gt;
            &lt;p&gt;&lt;/p&gt;
            &lt;input type="checkbox" id="start-checkbox"&gt; &lt;b&gt;I agree to start the quiz&lt;/b&gt;
            &lt;center&gt;
                &lt;button id="start-button" onclick="startQuiz()"&gt;Start Quiz&lt;/button&gt;
            &lt;/center&gt;
        &lt;/div&gt;
  
        &lt;!-- Add this HTML for the modal dialog --&gt;
        &lt;div id="myModal" class="modal"&gt;
              &lt;div class="modal-content"&gt;
                  &lt;h2&gt;Quiz Submission Confirmation&lt;/h2&gt;
                  &lt;p&gt;Do you really want to submit this quiz?&lt;/p&gt;
                  &lt;button id="confirmSubmit"&gt;Submit Quiz&lt;/button&gt;
                  &lt;button id="cancelSubmit"&gt;Cancel&lt;/button&gt;
              &lt;/div&gt;
        &lt;/div&gt;
        &lt;div id="fullscreen-container"&gt;
            &lt;div id="container" style="display: none; width: 100%;"&gt;
                &lt;div id="cont"&gt;
                    &lt;div id="quiz-container" style="display: none; "&gt;
                        &lt;div class="category-calculator"&gt;
                            &lt;div class="quiz-attempt-title" style="float: left;"&gt;
                                &lt;p&gt;GATE Aerospace Mock Test &lt;/p&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;div style="clear:both;"&gt;&lt;/div&gt;
                        &lt;div id="timer" style="float: right; font-size: 13px; display: block; font-weight: bold; "&gt;&lt;b&gt;Time Left: 35:00&lt;/b&gt;&lt;/div&gt;

                        &lt;hr&gt;
                        &lt;!-- Question 1 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 1 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Negative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The unruly crowd demanded that the accused be _____________ without trial.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options1" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Hung&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options1" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Hanged&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options1" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Hanging&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options1" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Hang&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;                        
                        &lt;!-- Question 2 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Updated Question 2 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Negative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;If A can complete a work in 20 days and B can complete the same work in 30 days, then how many days will it take for A and B together to complete the work?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;12 days&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;15 days&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options2" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;18 days&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;12 days&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 3 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 3 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A window is made up of a square portion and an equilateral triangle portion above it. The
                                base of the triangular portion coincides with the upper side of the square. If the perimeter of
                                the window is 6 m, the area of the window in m&lt;sup&gt;2&lt;/sup&gt; is ___________&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options3" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;1.43&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options3" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;2.06&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options3" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;2.68&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options3" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;2.88&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 4 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 4 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7
                                km away from where I live. Arun is farther away than Ahmed but closer than Susan from
                                where I live. From the information provided here, what is one possible distance (in km) at
                                which I live from Arun’s place ?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options4" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;3.00&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options4" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;4.99&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options4" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;6.02&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options4" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;7.01&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 5 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 5 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Which of the following is &lt;b&gt;CORRECT&lt;/b&gt; with respect to grammar and usage?
                                Mount Everest is ____________.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;the highest peak in the world&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;highest peak in the world&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;one of highest peak in the world&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt; one of the highest peak in the world&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 6 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.66" data-question-score="2" data-type="MCQ" data-explanation="Explanation for Question 6 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.66&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A person moving through a tuberculosis prone zone has a 50% probability of becoming
                                infected. However, only 30% of infected people develop the disease. What percentage of
                                people moving through a tuberculosis prone zone remains infected but does not show
                                symptoms of disease?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options6" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;24&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options6" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;15&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options6" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;33&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options6" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;35&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 7 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.66" data-question-score="2" data-type="MCQ" data-explanation="Explanation for Question 7 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.66&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela.
                                When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins
                                more often than Leela does. Which one of the following statements must be TRUE based
                                on the above?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options7" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;When Shiva plays chess with Leela and Pavithra, he often loses&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options7" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Leela is the oldest of the three&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options7" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Shiva is a better chess player than Pavithra&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options7" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Pavithra is the youngest of the three&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 8 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.66" data-question-score="2" data-type="MCQ" data-explanation="Explanation for Question 8 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.66&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone
                                for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day.
                                Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18
                                hours a day on all days. What is the ratio of work done by Q and R after 7 days from the
                                start of the project?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;20:21&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;10:11&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;11:10&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;21:20&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 9 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.66" data-question-score="2" data-type="MCQ" data-explanation="Explanation for Question 9 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.66&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;If q&lt;sup&gt;-a&lt;/sup&gt; = 1/r and r&lt;sup&gt;-b&lt;/sup&gt; = 1/s and s&lt;sup&gt;-c&lt;/sup&gt; = 1/q, the value of abc is __________&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options9" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;0&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options9" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;(rqs)&lt;sup&gt;-1&lt;/sup&gt;&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options9" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;1&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options9" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;rqs&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 10 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="2" data-incorrect-score="-0.66" data-question-score="2" data-type="MCQ" data-explanation="Explanation for Question 10 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Negative Marks: &lt;span style="color: red"&gt;0.66&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A car travels from point A to B at a speed of 60 km/hr and returns from B to A at a speed of 40 km/hr. What is the average speed of the car during the whole journey?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options10" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;45 km/hr&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options10" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;50 km/hr&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options10" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;48 km/hr&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options10" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;52 km/hr&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 11 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 11 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;11. If φ(x)= \( \int_{0}^{x^2} \sqrt{t} \,dt \) then  dφ/dx = ___&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options11" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;2x&lt;sup&gt;2&lt;/sup&gt;&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options11" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;&amp;radic;x&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options11" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;0&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options11" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;1&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 12 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 12 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;12. The value of \( \lim_{{x \to 0}} \frac{{1-cos(x^2)}}{{2x^4}} \)&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options12" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;0&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options12" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;1/2&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options12" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;1/4&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options12" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Undefined&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 13 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 13 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The Newton- Raphson method is to be used to find the root of the equation and f’(x) is&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options13" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt; always&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options13" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;only if f is a polynomial&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options13" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt; only if f(x&lt;sub&gt;0&lt;/sub&gt;)&lt;0&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options13" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;none of the above&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 14 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 14 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The necessary and sufficient condition for the differential equation of the form
                                M(x,y)dx+ N(x,y) dy = 0 to be exact is&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options14" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;M = N&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options14" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;\( \frac{\partial M}{\partial x} = \frac{\partial N}{\partial y} \)&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options14" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;\( \frac{\partial N}{\partial x} = \frac{\partial M}{\partial y} \)&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options14" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;\( \frac{\partial^2 M}{\partial^2 x} = \frac{\partial^2 N}{\partial^2 y} \)&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 15 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 15 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Solve for y if \( \frac{d^2 y}{dt^2} \)+2\( \frac{dy}{dt} \)+y = 0 with y(0)=1 and y'(0)= -2&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;(1-t)e^-t&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options15" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;(1+t)e^t&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;(1+t)e^-t&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;(1-t)e^t&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 16 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 16 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;16.  A Newtonian fluid has the following velocity field:
                                V = x&lt;sup&gt;2&lt;/sup&gt;yi + xy&lt;up&gt;2&lt;/up&gt;zj - yz&lt;sup&gt;3&lt;/sup&gt;k
                                The rate of shear deformation ε&lt;sub&gt;yz&lt;/sub&gt; at the point x = −2,
                            y = −l and z = 2 for the given flow is&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options16" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;-2&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options16" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;-6&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options16" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;-12&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options16" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;4&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 17 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The combustion process in a pulse-jet engine during ideal operation is:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options17" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;isentropic&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options17" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;isobaric&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options17" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;isochoric&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options17" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;isothermal&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 18 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 18 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The shape of a subsonic diffuser that slows down a  subsonic flow to supersonic flow is&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options18" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;converging&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options18" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;diverging&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options18" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;diverging–converging&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options18" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;converging–diverging&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 19 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Which of the following statement is &lt;b&gt;false&lt;/b&gt; with regards to Kutta condition for flow past airfoils?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options19" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;It is utilized to determine the circulation on an airfoil&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options19" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;The trailing edge of an airfoil is a stagnation point&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options19" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;The flow leaves the trailing edge smoothly&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options19" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;It is applicable only to airfoils with sharp trailing edge&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 20 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 20 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                        
                            &lt;/div&gt;
                            &lt;p&gt;What does the negative limit load factor represent in a V-n diagram?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options20" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;The maximum load factor in a dive&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options20" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;The maximum load factor in level flight&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options20" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;The maximum load factor in a climb&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options20" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;The maximum load factor in an inverted flight&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 21 --&gt;
                        &lt;div class="question nat-question" data-answer="0.125" data-correct-range="0.12;0.13" data-correct-score="1" data-incorrect-score="0" data-question-score="1" data-type="NAT" data-explanation="Explanation for Question 21 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Negative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Suppose that the eigen values of matrix A are 1, 2, 4. The determinant of (A&lt;sup&gt;-1&lt;/sup&gt;)&lt;sup&gt;T&lt;/sup&gt; is ____&lt;/p&gt;
                            &lt;textarea id="nat-answer21" name="nat-answer21" type="number" rows="4" cols="50" placeholder="Type your answer here" readonly&gt;&lt;/textarea&gt;
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer21')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer21')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer21')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer21',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 22 --&gt;
                        &lt;div class="question nat-question" data-answer="1.57" data-correct-range="1.50;1.60" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The error in numerically computing the integral \[ \int_{0}^{\pi} (sin{x}+cos{x}) \,dx\] using the trapezoidal
                                rule with three intervals of equal length between 0 and π  is __________&lt;/p&gt;
                            &lt;textarea id="nat-answer22" name="nat-answer22" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer22')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer22')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer22')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer22',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 23 --&gt;
                        &lt;div class="question nat-question" data-answer="5.75" data-correct-range="5.60;5.80" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An unpowered glider is flying at a glide angle of 10 degrees. Its lift-to-drag ratio is (round off to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer23" name="nat-answer23" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer23')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer23')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer23')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer23',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 24 --&gt;
                        &lt;div class="question nat-question" data-answer="6" data-correct-range="5.7;6" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;In a static test, a turbofan engine with bypass ratio of 9 has core hot exhaust speed
                                1.5 times that of fan exhaust speed. The engine is operated at a fuel to air ratio of
                                f = 0.03. Both the fan and the core streams have no pressure thrust. The ratio of
                                fan thrust to thrust from the core engine is _____ (round off to one decimal place).&lt;/p&gt;
                            &lt;textarea id="nat-answer24" name="nat-answer24" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer24')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer24')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer24')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer24',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 25 --&gt;
                        &lt;div class="question nat-question" data-answer="25" data-correct-range="25;25" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An aircraft weighing 10000 N is flying level at 100 m/s and it is powered by a jet engine. The thrust
                                required for level flight is 1000 N. The maximum possible thrust produced by the jet engine is 5000
                                N. The minimum time required to climb 1000 m, when flight speed is 100 m/s, is ________s.&lt;/p&gt;
                            &lt;textarea id="nat-answer25" name="nat-answer25" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer25')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer25')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer25')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer25',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 26 --&gt;
                        &lt;div class="question nat-question" data-answer="1.0" data-correct-range="1.0;1.0" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The governing differential equation of motion of a damped system is given by m(d&lt;sup&gt;2&lt;/sup&gt;x/dt&lt;sup&gt;2&lt;/sup&gt;)+c(dx/dt)+k = 0 . If m = 1 kg, c = 2 Ns/m and k = 2 N/m then the frequency of the damped
                                oscillation of this system is ____ rad/s.&lt;/p&gt;
                            &lt;textarea id="nat-answer26" name="nat-answer26" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer26')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer26')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer26')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer26',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 27 --&gt;
                        &lt;div class="question nat-question" data-answer="0.98" data-correct-range="0.98;0.98" data-correct-score="1" data-incorrect-score="0" data-question-score="1" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The stagnation pressures at the inlet and exit of a subsonic intake are 100 kPa and 98 kPa, respectively. The pressure recovery of this intake will be ______ (accurate to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer27" name="nat-answer27" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer27')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer27')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer27')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer27',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 28 --&gt;
                        &lt;div class="question nat-question" data-answer="0.5" data-correct-range="0.5;0.5" data-correct-score="1" data-incorrect-score="0" data-question-score="1" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A combustor is operating with a fuel-air ratio of 0.03. If the stoichiometric fuel-air ratio of
                                the fuel used is 0.06, the equivalence ratio of the combustor will be _______ (accurate to
                                two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer28" name="nat-answer28" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer28')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer28')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer28')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer28',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 29 --&gt;
                        &lt;div class="question nat-question" data-answer="7801" data-correct-range="7800;7802" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A spacecraft forms a circular orbit at an altitude of 150 km above the surface of a spherical
                                Earth. Assuming the gravitational parameter, μ = 3.986 × 10&lt;sup&gt;14&lt;/sup&gt;&gt; m&lt;sup&gt;3&lt;/sup&gt;
                                /s&lt;sup&gt;2&lt;/sup&gt;
                                and radius of earth,
                                RE = 6,400 km, the velocity required for the injection of the spacecraft, parallel to the local
                                horizon, is _______________ .&lt;/p&gt;
                            &lt;textarea id="nat-answer29" name="nat-answer29" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer29')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer29')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer29')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer29',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 30 --&gt;
                        &lt;div class="question nat-question" data-answer="3" data-correct-range="3;3" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The sytem of equations&lt;/p&gt;
                            &lt;p&gt;x-2y+az = 0&lt;/p&gt;
                            &lt;p&gt;2x+y-4z = 0&lt;/p&gt;
                            &lt;p&gt;x-y+z = 0&lt;/p&gt;
                            &lt;p&gt;has a non-trivial solution for a = ____ (Answer in integer)&lt;/p&gt;
                            &lt;textarea id="nat-answer30" name="nat-answer30" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer30')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer30')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer30')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer30',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 31 --&gt;
                        &lt;div class="question" data-answer="A;B;C" data-correct-score="2" data-incorrect-score="-0.33" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;What of the the following statement(s) is/are true about harmonically excited forced vibration of a single degree of freedom linear spring mass damper system?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options31" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;The total response of the mass is a combination of freee vibration transient and steady-state response&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options31" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped and over-damped)&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options31" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options31" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;The rate of decay of free vibration transient response depends on the mass, spring stiffness and damping coefficient&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 32 --&gt;
                        &lt;div class="question" data-answer="A;D" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;How does the propulsion efficiency of a ramjet engine, operating at a given Temperature and a given Altitude, change with increase in compressor pressure ratio?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options32" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;Remains constant&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options32" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;Increases monotonically&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options32" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;First decreases and then increases&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options32" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;Not affected by compressor pressure ratio&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 33 --&gt;
                        &lt;div class="question" data-answer="A;C;D" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Across an moving normal shock wave in a calorifically perfect gas, property does not change?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options33" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;the stagnation enthalpy changes&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options33" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt; the stagnation entropy changes&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options33" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;the stagnation temperature changes&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options33" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt; the speed of sound changes&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 34 --&gt;
                        &lt;div class="question nat-question" data-answer="12" data-correct-range="12;12" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A cantilever beam having a rectangular cross-section of width 60 mm and depth 100 mm, is
                                made of aluminum alloy. The material mechanical properties are: Young’s modulus,
                                E = 73 GPa and ultimate stress, σ&lt;sub&gt;u&lt;/sub&gt; = 480 MPa. Assuming a factor of safety of 4, the
                                maximum bending moment (in kN-m) that can be applied on the beam is _____ (accurate to
                                one decimal place).&lt;/p&gt;
                            &lt;textarea id="nat-answer34" name="nat-answer34" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer34')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer34')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer34')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer34',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 35 --&gt;
                        &lt;div class="question nat-question" data-answer="216" data-correct-range="215;216.5" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An axial compressor rotor with 50 % degree of reaction, operates with an axial velocity of
                                200 m/s. The absolute flow angle at the inlet of the rotor is 22&lt;sup&gt;o&lt;/sup&gt; with reference to the axial
                                direction. If the axial velocity is assumed to remain constant through the rotor, the magnitude
                                of the relative velocity (in m/s) at the rotor exit is __________ (accurate to one decimal
                                place).&lt;/p&gt;
                            &lt;textarea id="nat-answer35" name="nat-answer35" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer35')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer35')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer35')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer35',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 36 --&gt;
                        &lt;div class="question nat-question" data-answer="0.201" data-correct-range="0.195;0.205" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An aircraft wind tunnel model, having a pitch axis mass moment of inertia (I&lt;sub&gt;yy&lt;/sub&gt;) of
                                0.014 kg-m&lt;sup&gt;2&lt;/sup&gt;, is mounted in such a manner that it has pure pitching motion about its centre
                                of gravity, where it is supported through a frictionless hinge. If the pitching moment (M)
                                derivative with respect to angle of attack (α), denoted by ‘M&lt;sub&gt;α&lt;/sub&gt;’, is -0.504 N-m/rad and the
                                pitching moment (M) derivative with respect to pitch rate (q), denoted by ‘M&lt;sub&gt;q&lt;/sub&gt;’, is
                                -0.0336 N-m/(rad/s), the damping ratio of the resulting motion due to an initial disturbance
                                in pitch angle is approximately _________ (accurate to three decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer36" name="nat-answer36" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer36')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer36')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer36')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer36',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 37 --&gt;
                        &lt;div class="question nat-question" data-answer="223" data-correct-range="222.0;225.0" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The relative velocity of air leaving a straight radial impeller of a centrifugal compressor is
                                100 m/s. If the impeller tip speed is 200 m/s, for a slip free operation, the absolute velocity
                                (in m/s) at the impeller exit is _________ (accurate to one decimal place).&lt;/p&gt;
                            &lt;textarea id="nat-answer37" name="nat-answer37" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer37')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer37')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer37')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer37',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 38 --&gt;
                        &lt;div class="question nat-question" data-answer="50" data-correct-range="47;53" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The boundary layer thickness at the location of a sensor on a flat plate in an incompressible,
                                laminar flow of air is required to be restricted to 1 mm for an effective measurement. If the
                                flow velocity is 20 m/s with 1 bar pressure, 300 K temperature, and 1.789×10&lt;sup&gt;-5&lt;/sup&gt; kg/(m-s)
                                viscosity, the maximum distance (in mm) of the sensor location from the leading edge is
                                ________ (accurate to one decimal place).&lt;/p&gt;
                            &lt;textarea id="nat-answer38" name="nat-answer38" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer38')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer38')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer38')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer38',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 39 --&gt;
                        &lt;div class="question nat-question" data-answer="2.45" data-correct-range="2.40;2.50" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Consider a 20&lt;sup&gt;o&lt;/sup&gt; half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 36&lt;sup&gt;o&lt;/sup&gt;, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer39" name="nat-answer39" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer39')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer39')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer39')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer39',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 40 --&gt;
                        &lt;div class="question nat-question" data-answer="19440.0" data-correct-range="19440.0;19440.0" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A pitot probe on an aircraft in a steady, level flight records a pressure of 55,000 N/m&lt;sup&gt;2&lt;/sup&gt;. The static pressure and density are 45,280 N/m&lt;sup&gt;2&lt;/sup&gt; and 0.6 kg/m&lt;sup&gt;3&lt;/sup&gt;, respectively. The wing area and the lift coefficient are 16 m&lt;sup&gt;2&lt;/sup&gt; and 2, respectively. The wing loading (in N/m&lt;sup&gt;2&lt;/sup&gt; ) on this aircraft is _________ (accurate to one decimal place).&lt;/p&gt;
                            &lt;textarea id="nat-answer40" name="nat-answer40" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer40')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer40')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer40')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer40',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 41 --&gt;
                        &lt;div class="question nat-question" data-answer="20" data-correct-range="19;21" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Two solid shafts P and Q made of same material transmit equal torque. Shaft P has a uniform circular cross section A and shaft Q has a uniform circular cross section of area 4A. If the maximum torsional shear stress developed in shaft P is 160 MPa, the maximum torsional shear stress developed (in MPa) in shaft Q is ____&lt;/p&gt;
                            &lt;textarea id="nat-answer41" name="nat-answer41" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer41')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer41')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer41')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer41',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 42 --&gt;
                        &lt;div class="question nat-question" data-answer="-3" data-correct-range="-3;-3" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The state of stress at a point in a body under plane stress condition is given as σ&lt;sub&gt;x&lt;/sub&gt;=5MPa, σ&lt;sub&gt;y&lt;/sub&gt;=-1MPa and τ&lt;sub&gt;xy&lt;/sub&gt;=4MPa. If one of the principal stresses at that point is 7 MPa, then the other non-zero principal stress (in MPa) is _____&lt;/p&gt;
                            &lt;textarea id="nat-answer42" name="nat-answer42" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer42')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer42')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer42')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer42',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 43 --&gt;
                        &lt;div class="question nat-question" data-answer="6.55" data-correct-range="6.50;6.60" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An aircraft with twin jet engines has the following specifications:
                                Thrust produced (per engine) = 8000 N
                                Spanwise distance between the two engines = 10 m
                                Wing area = 50 m&lt;sup&gt;2&lt;/sup&gt;, Wing span = 10 m
                                Rudder effectiveness, Cnδr = −0. 002 /deg
                                Density of air at sea level = 1.225 kg/m&lt;sup&gt;3&lt;/sup&gt;
                                The rudder deflection, in degrees, required to maintain zero sideslip at 100
                                m/s in steady and level flight at sea level with a non-functional right engine
                                is ________ (round off to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer43" name="nat-answer43" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer43')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer43')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer43')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer43',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 44 --&gt;
                        &lt;div class="question nat-question" data-answer="210.00" data-correct-range="209.00;211.00" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An aircraft with a gross weight of 2000 kg, has a speed of 130 m/s at sea level, where the
                                conditions are: 1 atmosphere (pressure), 288 K (temperature), and 1.23 kg/m&lt;sup&gt;3&lt;/sup&gt; (density). The
                                speed (in m/s) required by the aircraft at an altitude of 9000 m, where the conditions are:
                                0.31 atmosphere, 230 K, and 0.47 kg/m&lt;sup&gt;3&lt;/sup&gt;, to maintain a steady, level flight is ________ (accurate to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer44" name="nat-answer44" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer44')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer44')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer44')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer44',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 45 --&gt;
                        &lt;div class="question nat-question" data-answer="-6.0" data-correct-range="-6.0;-6.0" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The components of stress in a body under plane stress condition, in the absence of body forces, is given by: σ&lt;sub&gt;xx&lt;/sub&gt; = Ax&lt;sup&gt;2&lt;/sup&gt;; σ&lt;sub&gt;yy&lt;/sub&gt; = 12x&lt;sup&gt;2&lt;/sup&gt;-6y&lt;sup&gt;2&lt;/sup&gt; and σ&lt;sub&gt;xy&lt;/sub&gt; = 12xy. The coefficient, A, such that the body is under equilibrium is _____ (accurate to one decimal
                                place).&lt;/p&gt;
                            &lt;textarea id="nat-answer45" name="nat-answer45" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer45')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer45')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer45')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer45',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 46 --&gt;
                        &lt;div class="question nat-question" data-answer="-2.40" data-correct-range="-2.50;-2.20" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A thin-walled tube with external radius of 100 mm and wall thickness of 2 mm, is fixed at
                                one end. It is subjected to a compressive force of 1 N acting at a point on the circumference
                                parallel to its length. The maximum normal stress (in kPa) experienced by the structure is
                                _____________ (accurate to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer46" name="nat-answer46" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer46')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer46')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer46')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer46',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 47 --&gt;
                        &lt;div class="question nat-question" data-answer="18.85" data-correct-range="18.80;18.90" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Gross weight of an airplane is 7000 N, wing area is 16 m&lt;sup&gt;2&lt;/sup&gt;, and the maximum lift coefficient is 2.0. Assuming density at the altitude as 1.23 kg/m&lt;sup&gt;3&lt;/sup&gt;, the stall speed (in m/s) of the aircraft is _________ (accurate to two decimal places).&lt;/p&gt;
                            &lt;textarea id="nat-answer47" name="nat-answer47" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer47')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer47')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer47')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer47',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 48 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Flow-separation from a solid surface may take place if the flow is:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options48" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;viscous, in a positive streamwise pressure gradient&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options48" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;viscous, in a negative streamwise pressure gradient&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options48" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;inviscid, in a positive streamwise pressure gradient&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options48" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;inviscid, in a negative streamwise pressure gradient&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 49 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The kind of fracture surface observed in a brittle specimen that fails under a uniaxial tensile test is:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options49" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Cup and cone&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options49" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Flat rough surface perpendicular to the axis of the specimen&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options49" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Helical rough surface with a 45&lt;sup&gt;o&lt;/sup&gt; inclination to the axis of the specimen&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options49" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Flat rough surface with a 45&lt;sup&gt;o&lt;/sup&gt; inclination to the axis of the specimen&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 50 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;&lt;img alt="" border="0" height="450px" width="500px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdFj2mrw0k9JZqpaSvy05RliI0J0kwIXl6-i5kCSxuMxNvWkS7aL5laDb6LfU9jC0JJOacoSbizqKOLcclGdp0qGiSgAHq35-muwPWaoGheFRBnYuvngjUoxUJlGCfuOaSIDHoGpNENTmv2EKAVlXA1nnUpaYzptHtYkkpwrLIEXalLPXhGesgC2yA61ti/s320/Som1.png"/&gt;&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options50" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;A&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options50" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;B&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options50" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;C&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options50" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;D&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 51 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;&lt;img alt="" border="0" height="450px" width="600px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Z-LgekqV6DngK-tlO4jbfqN8oq9-1Dno1J9d69K-pAFC7-1go3C5q0iGjv61rHkLCJLF5ikmP8tTHFl__XnIgvRD1t9B8-jCkjrkCo7cwsXAwxsX8hVewmqq502BDWeVUuaMwgpwLv_5duaSU6x1Bke49HNehGbNIGRSRKtbwmBDo-Hb96aMapi7nTDv/s1600/Som2.png"/&gt;&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options51" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;A&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options51" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;B&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options51" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;C&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options51" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;D&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 52 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;&lt;img alt="" border="0" height="450px" width="600px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs089-Gev0yf4Gh3lODLcZsoBqxTCEcuemnyB2BS1Q4MGDMljhVazvt4cOAqJAKi6Qlh_1FSZyvdQa2MLrz1nJAnyJk4r3finByYR-fzsMzeJOa1AfNaY1o21ges_OMSFS-ewV7D9EKB8K0dt2TnpXUjo7GHL_-IAdO8_flIDdcABzZYM46gUEj12kRngF/s1600/Som3.png"/&gt;&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options52" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;A&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options52" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;B&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options52" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;C&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options52" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;D&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 53 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;&lt;img alt="" border="0" width="auto" height="auto" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC8Rnp0yzaXDziwDmuJQ1g7b6jsvgEg4ajkN2ly6vv6yvk-tdzqJyaa3_I_vJst1fl7Fkbv_yy_4HH9Fg6SjVVqhpMtkGXfEjKlIssP7jHtOMNfVsdeh_zfx8VVApCFVJ_jND3LwvhZKzg2sUvwRU3VA6lJ10dCwr6SUSFbG5oRoIvCuhxOTkW-1Qj5XU3/s1600/Propulsion1.png"/&gt;&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options53" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;A&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options53" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;B&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options53" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;C&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options53" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;D&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 54 --&gt;
                        &lt;div class="question" data-answer="B;C;D" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Which of thr following statement(s) is/are true about the ribs of an airplane wing with semi-monocoque construction?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options54" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;For a rectangular platform wing, the dimensions of the ribss &lt;b&gt;DO NOT&lt;/b&gt; depend on their spanwise position in the wing.&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options54" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;Ribs increase the column buckling stress of longitudunal stiffeners connected to them&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options54" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;Ribs increase plate buckling stress of the skin panels&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options54" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;Ribs help in maintaing arodynamic shape of the wing&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 55 --&gt;
                        &lt;div class="question" data-answer="A;C;D" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options55" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;The buckling load increases with increase in flexural rigidity of the column&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options55" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;The buckling load increases with increase in the length of the column&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options55" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;The boundary conditions of the column affect the buckling load&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options55" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;The buckling load is NOT directly dependent on the density of the material used for the column&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 56 --&gt;
                        &lt;div class="question" data-answer="A;B;C;D" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Which of the following statement(s) is/are true about the state of stress in a plane?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options56" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;Maximum or major principal stress algebraically the largest direct stress at a point&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options56" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;The magnitude of minor principal stress cannot be greater than the magnitude of major principal stress&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options56" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;The planes of maximum shear stress are inclined at 90&lt;sup&gt;o&lt;/sup&gt; to the principal axes&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options56" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;The normal stresses along the planes of maximum shear stress are equal&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 57 --&gt;
                        &lt;div class="question" data-answer="A;B;C;D" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="MSQ" data-explanation="Explanation for Question 19 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Select Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;From the opions given. select all that are true for turbofan engines with afterburners.&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option1" name="msq-options56" type="checkbox" value="A" /&gt;
                                    &lt;label for="msq-option1"&gt;Turning afterburner ON increases specific fuel consumption&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option2" name="msq-options56" type="checkbox" value="B" /&gt;
                                    &lt;label for="msq-option2"&gt;Turbofan engines with afterburners have variable area nozzle&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option3" name="msq-options56" type="checkbox" value="C" /&gt;
                                    &lt;label for="msq-option3"&gt;Turning afterburner ON decreases specific fuel consumption&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="msq-option4" name="msq-options56" type="checkbox" value="D" /&gt;
                                    &lt;label for="msq-option4"&gt;Turning afterburner ON increase stagnation pressure across the engine&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 58 --&gt;
                        &lt;div class="question nat-question" data-answer="0.645" data-correct-range="0.640;0.650" data-correct-score="2" data-incorrect-score="0" data-question-score="2" data-type="NAT" data-explanation="Explanation for Question 22 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Non-Subjective (NAT)&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;2&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0&lt;/span&gt;
                                &lt;/span&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The idealized cross section of a thin walled wing box structure shown in the figure is subjected to an anticlockwise torque of 10 kNm. The corresponding shear flow distribution under this loading condition is hown in the figure. The area of each cell is A&lt;sub&gt;1&lt;/sub&gt;=300x10&lt;sup&gt;3&lt;/sup&gt; mm&lt;sup&gt;2&lt;/sup&gt; and A&lt;sub&gt;2&lt;/sub&gt;=250x10&lt;sup&gt;3&lt;/sup&gt; mm&lt;sup&gt;2&lt;/sup&gt;. The ratio of the unknowns x/y is given by ______ (in three decimal places).&lt;/p&gt;
                            &lt;p&gt;&lt;img alt="" border="0" data-original-height="266" data-original-width="519" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgYbO1xy9XkKMlkXCEb5ReLxs6VBW1R30Aw2t5lZdsCEAOHlsVjfMxXFqW6emKGqUobglC239dgr8mnDWUQN3FyMOPXHUQYYMEPeGDftFawtWLy9Be7kDxWrTRU9-WBqpjTT62UCd6mwtouozo6THwc0O1X6E-Z1q8xoh4KoJmsnW-GnTbstNjLE0d1vzf/s1600/Str1.png"/&gt;&lt;/p&gt;
                            &lt;textarea id="nat-answer58" name="nat-answer58" type="number" rows="4" cols="50" placeholder="Type your answer here"redonly&gt;&lt;/textarea&gt;                        
                            &lt;div class="numeric-keyboard" id="numeric-keyboard"&gt;
                                &lt;table border="0"&gt;
                                    &lt;tr&gt;
                                        &lt;td colspan="4"&gt;&lt;button onclick="clearTextarea('nat-answer58')"&gt;Clear&lt;/button&gt;&lt;/td&gt;                        
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',1)"&gt;1&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',2)"&gt;2&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',3)"&gt;3&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDecimal('nat-answer58')"&gt;.&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',4)"&gt;4&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',5)"&gt;5&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',6)"&gt;6&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="toggleNegative('nat-answer58')"&gt;+/-&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                    
                                    &lt;tr&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',7)"&gt;7&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',8)"&gt;8&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',9)"&gt;9&lt;/button&gt;&lt;/td&gt;
                                        &lt;td&gt;&lt;button onclick="appendDigit('nat-answer58',0)"&gt;0&lt;/button&gt;&lt;/td&gt;
                                    &lt;/tr&gt;                                                          
                                &lt;/table&gt;
                            &lt;/div&gt;     
                        &lt;/div&gt;
                        &lt;!-- Question 59 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The roots obtained by solving longitudinal characteristic equations of motion for a statically stable aircraft are given below:&lt;/p&gt;
                            &lt;p&gt;λ&lt;sub&gt;1,2&lt;/sub&gt;=-0.02 ± 0.30&lt;i&gt;i&lt;/i&gt;, λ&lt;sub&gt;3,4&lt;/sub&gt;=-2.00 ± 2.50&lt;i&gt;i&lt;/i&gt;, where &lt;i&gt;i&lt;/i&gt;=√-1&lt;/p&gt;
                            &lt;p&gt;the undaped shord-period longitudinal natural frequency (radians/sec) and damping ratio. in that order, are close to&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options59" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;3.40, 0.73&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options59" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;3.36, 0.65&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options59" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;3.83, 0.56&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options59" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;3.20, 0.63&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 60 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.66" data-question-score="2" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;An aircraft landing gear can be idealized as a single degree of freedom spring mass damper system. The desirable damping characteristics of such a system is:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options60" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Under damped&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options60" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Over damped&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options60" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Critically dapmed&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options60" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Undamped&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 61 --&gt;
                        &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options61" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Short period&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options61" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Phugoid&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options61" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Dutch roll&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options61" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Spiral&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 62 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A rocket nozzle is designed to produce maximum thrust at an altitude, H = 8 km from sea level. The nozzle operates in&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options62" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Under-expanded condition for H &gt; 8 km&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options62" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Under-expanded condition for H &lt; 8 km&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options62" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Sonic exit condition for H &gt; 8 km&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options62" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Unchoked condition for H &lt; 8 km&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 63 --&gt;
                        &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily. As a result, the center of pressure of the aircraft&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options63" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Shifts forward&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options63" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Shift rearward&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options63" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;does not shift&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options63" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;coincide with the neutral point&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 64 --&gt;
                        &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The function y=x&lt;sup&gt;3&lt;/sup&gt;-x has&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options64" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;No inflection point&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options64" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;One inflection point&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options64" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Two inflection point&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options64" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Three inflection point&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                        &lt;!-- Question 65 --&gt;
                        &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ" data-explanation="Explanation for Question 17 &lt;iframe width='560' height='315' src='https://www.youtube.com/embed/VIDEO_ID' frameborder='0' allowfullscreen&gt;&lt;/iframe&gt;"&gt;
                            &lt;div class="question-info"&gt;
                                &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                                &lt;span class="question-marks"&gt;
                                    Marks for correct answer: &lt;span style="color: green"&gt;1&lt;/span&gt; |
                                    Nagative Marks: &lt;span style="color: red"&gt;0.33&lt;/span&gt;
                                &lt;/span&gt;
                                &lt;div&gt;&lt;br&gt;&lt;/div&gt;
                            &lt;/div&gt;
                            &lt;p&gt;The stoichiometric fuel to air ratio in an aircraft engine combustor varies with the compressor pressure ratio as follows:&lt;/p&gt;
                            &lt;div class="options"&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option1" name="mcq-options65" type="radio" value="A" /&gt;
                                    &lt;label for="mcq-option1"&gt;Increases linearly&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option2" name="mcq-options65" type="radio" value="B" /&gt;
                                    &lt;label for="mcq-option2"&gt;Decreases linearly&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option3" name="mcq-options65" type="radio" value="C" /&gt;
                                    &lt;label for="mcq-option3"&gt;Is independent&lt;/label&gt;
                                &lt;/div&gt;
                                &lt;div&gt;
                                    &lt;input id="mcq-option4" name="mcq-options65" type="radio" value="D" /&gt;
                                    &lt;label for="mcq-option4"&gt;Increases non-linearly&lt;/label&gt;
                                &lt;/div&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;


                        &lt;!-- Progress indicator --&gt;
                        &lt;div id="progress"&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;!-- Question Index Section --&gt;
                    &lt;div id="question-index-container" style="overflow-y: auto; float: left; width: 24%; margin-left: 70%;  background-color: #413f3f;"&gt;
                        &lt;!-- Add an image at the top --&gt;
                        &lt;h1 style="width: 100%; margin-bottom: 10px; text-align: center; color: #f0f0f0;background-color: #0a0a0a;"&gt;AERO GATE TOPPER&lt;/h1&gt;

                        &lt;!-- Aptitude Section --&gt;
                        &lt;div class="question-section" id="aptitude-section" &gt;
                            &lt;h3 style="text-align: center; background-color: #f8f3f3e1;"&gt;Aptitude&lt;/h3&gt;
                            &lt;div id="aptitude-question-buttons" class="question-buttons"&gt;
                                &lt;!-- Generate Aptitude question buttons dynamically for questions 1 to 10 --&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;

                        &lt;!-- Core Section --&gt;
                        &lt;div class="question-section" id="core-section"&gt;
                            &lt;h3 style="text-align: center; background-color: #f8f3f3e1;"&gt;Core&lt;/h3&gt;
                            &lt;div id="core-question-buttons" class="question-buttons"&gt;
                                &lt;!-- Generate Core question buttons dynamically for remaining questions --&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;

                    &lt;div id="footer_buttons" style="display: none; margin-bottom: 0px;"&gt;
                        &lt;hr&gt;
                        &lt;!-- Previous, Next, and Submit buttons --&gt;
                        &lt;button id="prev"&gt;Previous&lt;/button&gt;
                        &lt;button id="next"&gt;Save &amp; Next&lt;/button&gt;
                        &lt;!-- &lt;button id="review" onclick="reviewQuestions()"&gt;Review&lt;/button&gt; --&gt;
                        &lt;button id="submit"&gt;Submit&lt;/button&gt;
                        &lt;button class="btn-sm btn-info" id="calc-btn" onClick="$('#calc').window('open');"&gt;&lt;img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirV3i0cTNot3yoHR1h9JSYpcw6XvXFE8_k_lWqrJc3In8C0QBsDD29cbmgckiV_JqwyA63f4fYGMu-gUk2pXRCG8wB7DWPD8mOFhlmU6Iaj2pSz7nTx8SI7ROAx6GLMvpDJpCH9N37lnAKJylJDXsmz6946S6qwTBIy8OCydd_ZRYUyk8whSWgK4mIwg/s1600/calc.png" alt="calc" height="20"&gt; Calculator &lt;/button&gt;
                        
                    &lt;/div&gt;

                &lt;/div&gt;

            &lt;/div&gt;
            &lt;div id="warning-popup" style="display: none;"&gt;
                &lt;p&gt;This is the last question. Are you sure you want to proceed?&lt;/p&gt;
                &lt;button id="confirm-warning"&gt;Yes&lt;/button&gt;
                &lt;button id="cancel-warning"&gt;No&lt;/button&gt;
            &lt;/div&gt;
    
            &lt;!-- Calculator container (initially hidden) --&gt;
            &lt;div id="calc-container" style="display: none;" draggable="true"&gt;
                &lt;div class="panel window window-thinborder c6 panel-htop" style="width: 480px;"&gt;
                    &lt;div class="panel-header panel-header-noborder window-header" style="width: 478px;"&gt;
                        &lt;div class="panel-icon icon-sum"&gt;&lt;/div&gt;
                        &lt;div class="panel-tool"&gt;
                            &lt;a href="javascript:;" class="panel-tool-collapse"&gt;&lt;/a&gt;
                            &lt;a href="javascript:;" class="panel-tool-close"&gt;&lt;/a&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                    &lt;div id="calc" class="easyui-window panel-body panel-body-noborder window-body"
                        title=""
                        style="width: 478px; height: 300px;"
                        data-options="iconCls:'icon-sum',minimizable:false,maximizable:false,resizable:false,border:'thin',cls:'c6',closed:true"&gt;
                        &lt;!-- Replace the URL with your calculator URL or embed code --&gt;
                        &lt;iframe src="https://shorturl.at/htFOS"
                            width="475px"
                            height="300px"
                            scrolling="no"
                            frameborder="0"&gt;
                        &lt;/iframe&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
            &lt;/div&gt;
        &lt;/div&gt;
  
        &lt;!-- Result section (initially hidden) --&gt;
        &lt;div id="result-container" style="display: none;"&gt;
              &lt;!-- Your result display code (remains the same) --&gt;
              &lt;div id="result"&gt;&lt;/div&gt;
  
              &lt;!-- Display user's score summary in a table --&gt;
              &lt;table id="score-summary"&gt;
                  &lt;thead&gt;
                      &lt;tr&gt;
                          &lt;th style="background:#337ab7;color:#ffffff;"&gt;Quiz Name&lt;/th&gt;
                          &lt;th style="background:#337ab7;color:#ffffff;"&gt;Score&lt;/th&gt;
                          &lt;th style="background:#337ab7;color:#ffffff;"&gt;Time Spend (Approx.)&lt;/th&gt;
                          &lt;th style="background:#337ab7;color:#ffffff;"&gt;Correct&lt;/th&gt;
                          &lt;th style="background:#337ab7;color:#ffffff;"&gt;Incorrect&lt;/th&gt;
                          &lt;th style="background:#337ab7;color:#ffffff;"&gt;Unattempted&lt;/th&gt;
                      &lt;/tr&gt;
                  &lt;/thead&gt;
                  &lt;tbody&gt;
                      &lt;tr&gt;
                          &lt;td style="font-weight: bold;"&gt;Mock Test&lt;/td&gt;
                          &lt;td id="user-score"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="total-time-taken"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="correct-answers"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="wrong-answers"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="unattempted"&gt;Calculating...&lt;/td&gt;
                      &lt;/tr&gt;
                  &lt;/tbody&gt;
              &lt;/table&gt;
  
  
              &lt;!-- Canvas for the chart --&gt;
              &lt;canvas height="200" id="resultChart" width="400"&gt;&lt;/canvas&gt;
        &lt;/div&gt;
  
        &lt;!-- Report section (initially hidden) --&gt;
        &lt;div id="report-container"&gt;
              &lt;!-- The report will be displayed here --&gt;
  
        &lt;/div&gt;

        &lt;script&gt;
            // Define quiz-related variables and constants
            let currentQuestion = 0;
            let questions = document.getElementsByClassName('question');
            let resultHTML = '';
            let timerInterval=0;
            const countdownMinutes = 185;
            let countdownSeconds = countdownMinutes * 60;
            let targetTime = Date.now() + countdownSeconds * 1000;
            const timeTakenArray = Array.from(questions).map(() =&gt; 0);
            const questionStartTimes = Array.from(questions).map(() =&gt; 0);
            const StartTime=0;


            window.addEventListener("load", function () {
                MathJax.typeset();
            });

            // Shuffle &amp; Numbering
            window.onload = function() {
                // Question Shuffle
                var questions = Array.from(document.getElementsByClassName('question'));
                var firstTenQuestions = questions.slice(0, 10);
                var remainingQuestions = questions.slice(10);

                // Shuffle first 10 questions
                for (var i = firstTenQuestions.length - 1; i &gt; 0; i--) {
                    var j = Math.floor(Math.random() * (i + 1));
                    firstTenQuestions[i].parentNode.insertBefore(firstTenQuestions[j], firstTenQuestions[i].nextSibling);
                }

                // Shuffle remaining questions
                for (var i = remainingQuestions.length - 1; i &gt; 0; i--) {
                    var j = Math.floor(Math.random() * (i + 1));
                    remainingQuestions[i].parentNode.insertBefore(remainingQuestions[j], remainingQuestions[i].nextSibling);
                }

                // Update the questions array to reflect the new order
                questions = Array.from(document.getElementsByClassName('question'));

                // Question Number Assign
                for (var i = 0; i &lt; questions.length; i++) {
                    var questionText = questions[i].getElementsByTagName('p')[0];
                    questionText.innerHTML = (i + 1) + '. ' + questionText.innerHTML;
                }
            }

            // block keyboard 
            window.addEventListener('keydown', function(e) {
                // List of keys you want to disable
                const keysToDisable = ['Tab', 'ArrowUp', 'ArrowDown', 'ArrowLeft', 'ArrowRight','Escape','1','2','3','4','5','6','7','8','9','0'];

                // Check if the key is an alphabet or in the list of keys to disable
                if ((e.key &gt;= 'a' &amp;&amp; e.key &lt;= 'z') || (e.key &gt;= 'A' &amp;&amp; e.key &lt;= 'Z') || keysToDisable.includes(e.key)) {
                    e.preventDefault();
                }
            }, false);

            // Start for numeric keyboard for a question
            function appendDigit(textareaId, digit) {
                const natTextarea = document.getElementById(textareaId);
                natTextarea.value += digit;
            }

            function appendDecimal(textareaId) {
                const natTextarea = document.getElementById(textareaId);
                if (!natTextarea.value.includes('.')) {
                    natTextarea.value += '.';
                }
            }

            function toggleNegative(textareaId) {
                const natTextarea = document.getElementById(textareaId);
                if (natTextarea.value.startsWith('-')) {
                    natTextarea.value = natTextarea.value.slice(1);
                } else {
                    natTextarea.value = '-' + natTextarea.value;
                }
            }

            function clearTextarea(textareaId) {
                const natTextarea = document.getElementById(textareaId);
                natTextarea.value = '';
            }

            document.querySelectorAll('.nat-answer').forEach(function (textarea) {
                const numericKeyboard = document.getElementById('numeric-keyboard' + textarea.id.slice(-2));

                textarea.addEventListener('focus', function () {
                    numericKeyboard.style.display = 'flex';
                });

                window.addEventListener('click', function (event) {
                    if (!textarea.contains(event.target) &amp;&amp; !numericKeyboard.contains(event.target)) {
                        numericKeyboard.style.display = 'none';
                    }
                });
            });

            // End for Numeric Keyboard for a question
            
            // Get references to the calculator button and container
            document.getElementById('calc-btn').addEventListener('click', function () {
                const calcContainer = document.getElementById('calc-container');
                
                // Toggle the display of the calculator container
                if (calcContainer.style.display === 'none' || calcContainer.style.display === '') {
                    calcContainer.style.display = 'block';
                } else {
                    calcContainer.style.display = 'none';
                }

                // Append the calcContainer to the fullscreen container
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.appendChild(calcContainer);
            });

            document.getElementById('start-button').addEventListener('click', function () {
                // Hide the start page and show the quiz container
                document.getElementById('start-page').style.display = 'none';
                document.getElementById('container').style.display = 'block';
                document.getElementById('quiz-container').style.display = 'block';
                document.getElementById('footer_buttons').style.display = 'block';

                // Load the first question to start the quiz
                 loadQuestion(0);                    
                // Start the countdown timer
                startCountdown();
            });
            
            // Update the question index list click event listener to use loadQuestion
            function generateQuestionButtons() {
                const aptitudeQuestionButtons = document.getElementById('aptitude-question-buttons');
                const coreQuestionButtons = document.getElementById('core-question-buttons');
                const questions = document.querySelectorAll('.question');
                for (let i = 0; i &lt; questions.length; i++) {
                    const button = document.createElement('button');
                    button.textContent = `${i + 1}`;  
                    // Add click event listener to load the question by index
                    button.addEventListener('click', () =&gt; {
                        recordTimeTaken(); // Record time taken before jumping to the new question
                        loadQuestion(i);
                    });
                    // Determine whether the question belongs to Aptitude or Core section
                    if (i &lt; 10) {
                        // Questions 1 to 10 go to Aptitude
                        aptitudeQuestionButtons.appendChild(button);
                    } else {
                        // Remaining questions go to Core, start counting from 1
                        button.textContent = `${i + 1}`;
                        coreQuestionButtons.appendChild(button);
                    }
                }
            }

            // Call the function to generate question buttons
            generateQuestionButtons();
            
            // Function to update the timer display
            function updateTimerDisplay() {
                const remainingTime = Math.max(0, targetTime - Date.now());
                const minutes = Math.floor(remainingTime / 1000 / 60);
                const seconds = Math.floor((remainingTime / 1000) % 60);
                const formattedTime = `${minutes.toString().padStart(2, '0')}:${seconds.toString().padStart(2, '0')}`;
                
                const timerElement = document.getElementById('timer');
                
                // Apply red color style if remaining time is less than 10 minutes
                if (minutes &lt; 10) {
                    timerElement.style.color = 'red';
                } else {
                    timerElement.style.color = ''; // Reset to default color
                }

                timerElement.textContent = `Time Left: ${formattedTime}`;
            }

            // Function to handle the timer countdown
            function startCountdown() {
                updateTimerDisplay();
                let timerInterval = setInterval(() =&gt; {
                    if (Date.now() &gt;= targetTime) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        showResult();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
                // Record the start time of the first question
                if (currentQuestion === 0) {
                    questionStartTimes[currentQuestion] = Date.now();
                }
            }

            startCountdown();

            // // Function to update the timer display
            // function updateTimerDisplay() {
            //     const minutes = Math.floor(countdownSeconds / 60);
            //     const seconds = countdownSeconds % 60;
            //     const formattedTime = `${minutes.toString().padStart(2, '0')}:${seconds.toString().padStart(2, '0')}`;
            //     document.getElementById('timer').textContent = `Time Left: ${formattedTime}`;
            // }

            // // Function to handle the timer countdown
            // function startCountdown() {
            //     updateTimerDisplay();
            //     timerInterval = setInterval(() =&gt; {
            //         countdownSeconds--;
            //         if (countdownSeconds &lt; 0) {
            //             clearInterval(timerInterval);
            //             document.getElementById('timer').textContent = "Time's Up!";
            //             showResult();
            //         } else {
            //             updateTimerDisplay();
            //         }
            //     }, 1000);
            //     // Record the start time of the first question
            //     if (currentQuestion === 0) {
            //         questionStartTimes[currentQuestion] = Date.now();
            //     }
            // }
            
            // Function to record the time taken for the current question
            
            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestion];
                const timeTaken = ((questionEndTime - questionStartTime) / 1000).toFixed(2); // Calculate time taken in seconds
                // Calculate cumulative time taken for the current question
                timeTakenArray[currentQuestion] = (timeTakenArray[currentQuestion] || 0) + parseFloat(timeTaken);
                // Update the start time for the current question
                questionStartTimes[currentQuestion] = questionEndTime;
            }

            // Function to load a question
            function loadQuestion(questionIndex) {
                for (let i = 0; i &lt; questions.length; i++) {
                    questions[i].style.display = 'none';
                }
                
                if (questionIndex &gt;= 0 &amp;&amp; questionIndex &lt; questions.length) {
                    currentQuestion = questionIndex;
                    questions[currentQuestion].style.display = 'block';
                
                    // Record the start time of the question if it's not set yet
                    if (!questionStartTimes[currentQuestion]) {
                        questionStartTimes[currentQuestion] = Date.now();
                    }
                
                    // Update the chart when loading a question
                    updateChart();
                
                    // Show the current question and hide the "Previous" and "Next" buttons as needed
                    showQuestion(currentQuestion);

                    // Start the countdown timer only if it's the first question
                    if (questionIndex === 0) {
                        startCountdown();
                    }
                    // Check if the question is NAT type and adjust the UI accordingly
                    const questionType = questions[currentQuestion].getAttribute('data-type');
                    if (questionType === 'NAT') {
                        // Hide the options for NAT type questions
                        const options = questions[currentQuestion].querySelector('.options');
                        if (options) {
                            options.style.display = 'none';
                        }
                    } else {
                        // Show the options for other question types
                        const options = questions[currentQuestion].querySelector('.options');
                        if (options) {
                            options.style.display = 'block';
                        }
                    }
                }
            }
            loadQuestion(0);

            function showQuestion(index) {
                for (var i = 0; i &lt; questions.length; i++) {
                    questions[i].style.display = i === index ? "block" : "none";
                }
                document.getElementById("prev").style.display = index === 0 ? "none" : "inline";
                document.getElementById("next").style.display = index === questions.length - 1 ? "none" : "inline";
            }

            // Add this function to show the warning popup
            function showWarningPopup() {
                const warningPopup = document.getElementById('warning-popup');
                warningPopup.style.display = 'block';

                // Handle the "Yes" button click inside the warning popup
                document.getElementById('confirm-warning').addEventListener('click', function () {
                    warningPopup.style.display = 'none';
            
                });

                // Handle the "No" button click inside the warning popup
                document.getElementById('cancel-warning').addEventListener('click', function () {
                    warningPopup.style.display = 'none';
                });
            }

            // Function to handle the "Previous" button click
            function prevQuestion() {
                recordTimeTaken();
                currentQuestion--;
                // Reset start time for new current question
                questionStartTimes[currentQuestion] = Date.now();
                showQuestion(currentQuestion);
                console.log(`Total time spent on this question: ${timeTakenArray[currentQuestion]} seconds`);

                // Enter fullscreen for the quiz container
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();                    
            }

            // Function to handle the "Next" button click
            function nextQuestion() {
                recordTimeTaken();
                currentQuestion++;
                // Reset start time for new current question
                questionStartTimes[currentQuestion] = Date.now();
                showQuestion(currentQuestion);
                console.log(`Total time spent on this question: ${timeTakenArray[currentQuestion]} seconds`);
                // Enter fullscreen for the quiz container
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                
            }

            // Function to handle the review of questions
            function reviewQuestions() {
                // Do any additional logic you need for the review process
                // For example, you can mark questions for review, display them differently, etc.
                // Here, let's simply log a message to the console for demonstration purposes
                recordTimeTaken();
                currentQuestion++;
                console.log('Reviewing questions...');
                // Reset start time for new current question
                questionStartTimes[currentQuestion] = Date.now();
                showQuestion(currentQuestion);
                console.log(`Total time spent on this question: ${timeTakenArray[currentQuestion]} seconds`);
                // Enter fullscreen for the quiz container
                const fullscreenContainer = document.getElementById('fullscreen-container');
                fullscreenContainer.requestFullscreen();

                // You might want to add specific styling or marks to questions that are under review
                // For instance, you can add a 'reviewed' class to the question elements:
                const reviewedQuestions = document.querySelectorAll('.question');
                reviewedQuestions.forEach(question =&gt; {
                    question.classList.add('reviewed');
                });
            }

            // Function to handle submitting the quiz
            function submitQuiz() {
                recordTimeTaken(); // Record time taken for the last question

                // Display the modal dialog when submitting the quiz
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';

                // Handle the "Yes" button click inside the modal
                document.getElementById('confirmSubmit').addEventListener('click', function() {
                    clearInterval(timerInterval); // Stop the timer only when submitting
                    modal.style.display = 'none';
                    showResult();
                });

                // Handle the "No" button click inside the modal
                document.getElementById('cancelSubmit').addEventListener('click', function() {
                    modal.style.display = 'none';
                    // Enter fullscreen for the quiz container
                    const fullscreenContainer = document.getElementById('fullscreen-container');
                    fullscreenContainer.requestFullscreen();                    
                });

                // Exit fullscreen after submitting the quiz
                const doc = window.document;
                const exitFullScreen = doc.exitFullscreen || doc.mozCancelFullScreen || doc.webkitExitFullscreen || doc.msExitFullscreen;
                exitFullScreen.call(doc);

                // Check if the last question is NAT type, and handle it accordingly
                const lastQuestionType = questions[currentQuestion].getAttribute('data-type');
                if (lastQuestionType === 'NAT') {
                    // Do something specific for NAT type questions, if needed
                }
            }

            // Function to calculate user's score for NAT, MCQ, and MSQ
            /* function calculateScore() {
                let userTotalScore = 0;
                let totalPossibleScore = 0;

                // Iterate through each question
                for (let i = 0; i &lt; questions.length; i++) {
                    const question = questions[i];
                    const questionType = question.getAttribute('data-type');
                    const correctAnswer = question.getAttribute('data-answer').split(';');
                    let userAnswer;

                    if (questionType === 'NAT') {
                        // For NAT type questions, get the user's answer from the textarea
                        userAnswer = question.querySelector('textarea').value.trim();
                    } else {
                        // For MCQ and MSQ type questions, get the user's selected options
                        userAnswer = Array.from(question.querySelectorAll('input:checked')).map(input =&gt; input.value).sort().join(';');
                    }

                    // Get the scoring values
                    const correctScore = parseFloat(question.getAttribute('data-correct-score'));
                    const incorrectScore = parseFloat(question.getAttribute('data-incorrect-score'));
                    const questionScore = parseFloat(question.getAttribute('data-question-score'));

                    // Calculate the question score
                    let score = 0;
                    if (userAnswer === correctAnswer.join(';')) {
                        // User's answer is correct
                        score = correctScore;
                    } else if (userAnswer !== '' &amp;&amp; userAnswer !== correctAnswer.join(';')) {
                        // User attempted the question but got it wrong
                        score = incorrectScore;
                    } else {
                        // User did not attempt the question
                        score = 0;
                    }

                    // Add the calculated score to the user's total score
                    userTotalScore += score;

                    // Add the question score to the total possible score
                    totalPossibleScore += questionScore;
                }

                return { userTotalScore, totalPossibleScore };
            } */

            // Function to display the result and report
            function showResult() {
                // Hide the quiz container and show the result and report containers
                document.getElementById('container').style.display = 'none';
                document.getElementById('quiz-container').style.display = 'none';
                document.getElementById('footer_buttons').style.display = 'none';
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('report-container').style.display = 'block';

                // Initialize variables for tracking correct, wrong, and unattempted questions
                let correctAnswers = 0;
                let wrongAnswers = 0;
                let unattempted = 0;
                let totalScore = 0;

                // Calculate user's score and update counts for correct, wrong, and unattempted questions
                for (let i = 0; i &lt; questions.length; i++) {
                    const question = questions[i];
                    let correctAnswer = question.getAttribute('data-answer').trim().toLowerCase().split(';');
                    let userAnswer;

                    if (question.getAttribute('data-type') === 'NAT') {
                        // Get the user's answer from the textarea
                        userAnswer = [question.querySelector('textarea').value.trim().toLowerCase()];
                    } else {
                        userAnswer = Array.from(question.querySelectorAll('input:checked')).map(input =&gt; input.value.trim().toLowerCase());
                    }

                    // Sort the answers before comparing
                    correctAnswer.sort();
                    userAnswer.sort();

                    // Check if the user attempted the question
                    const isAttempted = userAnswer.join(';') !== '';

                    if (isAttempted) {
                        if (question.getAttribute('data-type') === 'NAT') {
                            // Check if the user's NAT answer is within the correct range
                            const correctRange = question.getAttribute('data-correct-range') ? question.getAttribute('data-correct-range').split(';') : null;
                            if (
                                correctRange &amp;&amp; parseFloat(userAnswer[0]) &gt;= parseFloat(correctRange[0]) &amp;&amp; parseFloat(userAnswer[0]) &lt;= parseFloat(correctRange[1])
                            ) {
                                // User's NAT answer is within the correct range
                                correctAnswers++;
                                totalScore += parseFloat(question.getAttribute('data-correct-score'));
                            } else {
                                // User's NAT answer is outside the correct range
                                wrongAnswers++;
                                totalScore += parseFloat(question.getAttribute('data-incorrect-score'));
                            }
                        } else {
                            // Check if the user's answer is correct for non-NAT questions
                            const isCorrect = userAnswer.join(';') === correctAnswer.join(';');

                            if (isCorrect) {
                                // User's answer is correct
                                correctAnswers++;
                                totalScore += parseFloat(question.getAttribute('data-correct-score'));
                            } else {
                                // User's answer is incorrect
                                wrongAnswers++;
                                totalScore += parseFloat(question.getAttribute('data-incorrect-score'));
                            }
                        }
                    } else {
                        // User did not attempt the question
                        unattempted++;
                    }
                }
                // Calculate total time taken
                const totalSeconds = timeTakenArray.reduce((acc, time) =&gt; acc + parseFloat(time), 0);
                const totalMinutes = Math.floor(totalSeconds / 60);
                const remainingSeconds = Math.round(totalSeconds % 60); // Round the remaining seconds to the nearest whole number
                const totalTimeTaken = `${totalMinutes} min ${remainingSeconds} sec`;

                // Update the table with the calculated values
                document.getElementById('user-score').textContent = totalScore.toFixed(2);
                document.getElementById('total-time-taken').textContent = totalTimeTaken;
                document.getElementById('correct-answers').textContent = correctAnswers;
                document.getElementById('wrong-answers').textContent = wrongAnswers;
                document.getElementById('unattempted').textContent = unattempted;


                // Initialize the resultHTML variable to store the report HTML
                let resultHTML = '';

                // Loop through questions to generate the report
                for (let i = 0; i &lt; questions.length; i++) {
                    const question = questions[i];
                    const correctAnswer = question.getAttribute('data-answer').split(';');
                    const correctRange = question.getAttribute('data-correct-range') ? question.getAttribute('data-correct-range').split(';') : null;
                    const selectedOptions = question.getAttribute('data-type') === 'NAT' ? [question.querySelector('textarea').value.trim()] : Array.from(question.querySelectorAll('input:checked')).map(input =&gt; input.value);
                    const userAnswer = selectedOptions.join(';');

                    // Function to check correctness based on question type
                    function isAnswerCorrect(userAnswer, correctAnswer, correctRange) {
                        if (correctRange) {
                            if (correctRange.length === 2) {
                                const isWithinRange = parseFloat(userAnswer) &gt;= parseFloat(correctRange[0]) &amp;&amp; parseFloat(userAnswer) &lt;= parseFloat(correctRange[1]);
                                return isWithinRange;
                            } else {
                                return userAnswer === correctAnswer.join(';');
                            }
                        } else {
                            return userAnswer === correctAnswer.join(';');
                        }
                    }

                    // Determine the class to apply for background color based on the user's answer
                    const isCorrect = isAnswerCorrect(userAnswer, correctAnswer, correctRange);
                    // Determine the class to apply for background color based on the user's answer
                    const backgroundClass = isCorrect ? 'correct-answer' : userAnswer === '' ? 'not-answered' : 'wrong-answer';

                    // Include an explanation for each question
                    const explanation = question.getAttribute('data-explanation');
                    const explanationHTML = explanation ? `&lt;p&gt;&lt;strong&gt;Explanation:&lt;/strong&gt; ${convertSpecialCharsToHTML(explanation)}&lt;/p&gt;` : '';
                    // Generate HTML for each question in the report
                    // Generate HTML for the report, including symbols
                    const resultSymbol = userAnswer === '' ? '❓' : userAnswer === correctAnswer.join(';') ? '✅' : '❌';

                    const correctRangeHTML = question.getAttribute('data-correct-range') ? `&lt;p&gt;&lt;strong&gt;Correct Range:&lt;/strong&gt; ${convertSpecialCharsToHTML(question.getAttribute('data-correct-range'))}&lt;/p&gt;`: '';

                    // Function to convert special characters to subscripts and superscripts
                    function convertSpecialCharsToHTML(text) {
                        return text
                        .replace(/&lt;sub&gt;/g, '_')
                        .replace(/&lt;sup&gt;/g, '^')
                        .replace(/_/g, '&lt;sub&gt;_&lt;/sub&gt;')
                        .replace(/\^/g, '&lt;sup&gt;^&lt;/sup&gt;');
                    }

                    const questionHTML = `
                        &lt;div class="question-report ${backgroundClass}"&gt;
                            &lt;div class="question-container ${backgroundClass}"&gt;
                                &lt;p&gt;Question Type: &lt;b&gt;${question.getAttribute('data-type')}&lt;/b&gt;&lt;/p&gt;
                                &lt;p&gt;
                                    Marks for correct answer:&amp;nbsp; &lt;span style="color: green"&gt;${question.getAttribute('data-correct-score')}&lt;/span&gt; 
                                    &amp;nbsp; | &amp;nbsp; 
                                    Negative Marks&amp;nbsp; &lt;span style="color: red"&gt;${question.getAttribute('data-incorrect-score')}&lt;/span&gt;
                                &lt;/p&gt;
                                &lt;p&gt;Question ${i + 1}&lt;/p&gt;
                                &lt;p&gt;${convertSpecialCharsToHTML(question.querySelector('p').innerHTML)}&lt;/p&gt;
                                ${
                                    question.getAttribute('data-type') === 'NAT'
                                        ? `
                                            &lt;p&gt;
                                                &lt;div class="options"&gt;
                                                    ${generateOptionsHTML(question)}
                                                &lt;/div&gt;
                                            &lt;/p&gt;
                                            &lt;p&gt;&lt;strong&gt;Your Answer:&lt;/strong&gt; ${convertSpecialCharsToHTML(userAnswer || 'Not answered')}&lt;/p&gt;
                                            &lt;p&gt;&lt;strong&gt;Correct Answer:&lt;/strong&gt; ${convertSpecialCharsToHTML(correctAnswer.join(';'))}&lt;/p&gt;
                                            ${correctRangeHTML}
                                            &lt;p&gt;&lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${userAnswer === '' ? 'Not attempted' : userAnswer === correctAnswer.join(';') ? 'Correct' : 'Wrong'}&lt;/p&gt;
                                        `
                                        : `
                                            &lt;p&gt;
                                                &lt;div class="options"&gt;
                                                    ${generateOptionsHTML(question)}
                                                &lt;/div&gt;
                                            &lt;/p&gt;
                                            &lt;p&gt;&lt;strong&gt;Your Answer:&lt;/strong&gt; ${convertSpecialCharsToHTML(userAnswer || 'Not answered')}&lt;/p&gt;
                                            &lt;p&gt;&lt;strong&gt;Correct Answer:&lt;/strong&gt; ${convertSpecialCharsToHTML(correctAnswer.join(';'))}&lt;/p&gt;
                                            ${correctRangeHTML}
                                            &lt;p&gt;&lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${userAnswer === '' ? 'Not attempted' : userAnswer === correctAnswer.join(';') ? 'Correct' : 'Wrong'}&lt;/p&gt;
                                        `
                                }
                            &lt;/div&gt;
                        &lt;/div&gt;
                    `;
                    resultHTML += questionHTML;
                }

                // Display the report in the report container
                document.getElementById('report-container').innerHTML = resultHTML;

                // Display the user's score
                const { userTotalScore, totalPossibleScore } = calculateScore();
                const userScoreText = `Your Score: ${userTotalScore.toFixed(2)} out of ${totalPossibleScore.toFixed(2)}`;
                document.getElementById('result').textContent = userScoreText;

                // Call the updateChart function to display the chart (assuming you have an updateChart function)
                updateChart();
            }

            // Function to generate HTML for options
            function generateOptionsHTML(question) {
                const optionsHTML = [];
                const options = question.querySelectorAll('input[type="radio"], input[type="checkbox"]');

                options.forEach((option) =&gt; {
                    const label = option.nextElementSibling;
                    optionsHTML.push(`
                        &lt;div&gt;
                            &lt;input type="${option.type}" value="${option.value}" ${option.checked ? 'checked' : ''} disabled&gt;
                            &lt;label&gt;${label.textContent}&lt;/label&gt;
                        &lt;/div&gt;
                    `);
                });

                return optionsHTML.join('');
            }

            // Event listeners for navigation buttons
            document.getElementById('prev').addEventListener('click', prevQuestion);
            document.getElementById('next').addEventListener('click', nextQuestion);
            document.getElementById('submit').addEventListener('click', submitQuiz);

            

            // Load the first question
            loadQuestion(0);

            // Show a warning when the user tries to leave the page (e.g., by refreshing)
            window.addEventListener('beforeunload', function (e) {
                e.preventDefault();
                e.returnValue = 'You have unsaved changes. Are you sure you want to leave?';
            });

            // Calculator Button Click Event
            document.getElementById('calculator').addEventListener('click', function () {
                // Implement calculator functionality here
                alert('Open Calculator');
            });

            // Function to update the chart
            function updateChart() {
                const ctx = document.getElementById('resultChart').getContext('2d');
                // Create a chart using Chart.js
                const chart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: timeTakenArray.map((_, index) =&gt; `Q ${index + 1}`),
                        datasets: [{
                            label: 'Time Taken (seconds)',
                            data: timeTakenArray,
                            backgroundColor: 'rgba(0, 123, 255, 0.7)',
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true,
                                title: {
                                    display: true,
                                    text: 'Time Spend (seconds)'
                                }
                            },
                            x: {
                                title: {
                                    display: true,
                                    text: 'Question Number'
                                }
                            }
                        },
                    }
                });
            }
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;</description><link>https://aerogatetopper.blogspot.com/2024/01/gate-aerospace-practice-mock-test-1.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdFj2mrw0k9JZqpaSvy05RliI0J0kwIXl6-i5kCSxuMxNvWkS7aL5laDb6LfU9jC0JJOacoSbizqKOLcclGdp0qGiSgAHq35-muwPWaoGheFRBnYuvngjUoxUJlGCfuOaSIDHoGpNENTmv2EKAVlXA1nnUpaYzptHtYkkpwrLIEXalLPXhGesgC2yA61ti/s72-c/Som1.png" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-419585792733215379</guid><pubDate>Sun, 03 Dec 2023 15:28:00 +0000</pubDate><atom:updated>2023-12-20T07:59:00.483+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Strength of material mock test</category><title>Stress in Beams</title><description>&lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"
     crossorigin="anonymous"&gt;&lt;/script&gt;
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     data-full-width-responsive="true"&gt;&lt;/ins&gt;
&lt;script&gt;
     (adsbygoogle = window.adsbygoogle || []).push({});
&lt;/script&gt;
&lt;p&gt;&lt;/p&gt;
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&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;

&lt;html lang="en"&gt;
    &lt;head&gt;
        &lt;title&gt;Online Quiz&lt;/title&gt;
        &lt;meta charset="UTF-8"&gt;&lt;/meta&gt;
        &lt;meta content="width=device-width, initial-scale=1.0" name="viewport"&gt;&lt;/meta&gt;
        &lt;script src="https://cdn.jsdelivr.net/npm/chart.js"&gt;&lt;/script&gt; 
        &lt;script src="https://cdnjs.cloudflare.com/ajax/libs/Chart.js/3.7.0/chart.min.js"&gt;&lt;/script&gt;

        &lt;script&gt;
       
            let quizStarted = false; // Variable to track if the quiz has started
            let resultDisplayed = false; // Variable to track if the result is displayed
        
            // Function to display a confirmation message when the user tries to leave the page
            window.onbeforeunload = function (e) {
                if (quizStarted || resultDisplayed) {
                    e.preventDefault();
                    e.returnValue = "Data will be lost if you leave the page, are you sure?";
                }
            };
        
            // Function to set quizStarted variable to true when the quiz starts
            function startQuiz() {
                quizStarted = true;
              
              // Enter fullscreen for the quiz container
        const quizContainer = document.getElementById('container');
        quizContainer.requestFullscreen();

            }   
        
            // Function to set resultDisplayed variable to true when the result is displayed
            function displayResult() {
                resultDisplayed = true;
            }
        &lt;/script&gt;

        &lt;style&gt; 
            body {
                font-family: Helvetica Neue,Helvetica,Arial,sans-serif;
                margin: auto;
                padding: 0;
                font-size: 14px;
                line-height: 1.42857143;
                color: #333;
                background-color: #f2f2f2;
            }

            #container {
                height: 600px;
                margin-left: 30px;
                margin-bottom: 30px;
                padding: 20px;
                background-color: #fff;
                box-shadow: 0 10px 30px rgba(0 0 0 / 96%);
                border-radius: 5px;
            }
            #quiz-container {
                overflow: auto;
                height: 500px;
          	    margin-left: 30px;
                margin-bottom: 30px;
                padding: 20px;
                background-color: #fff;
            
            }

            .question {
                margin-top: 10px;
                display: none;
                width: 90%;;
                margin-bottom: 20px;
            }

            h1 {
                font-size: 20px;
                margin-top: 20px;
                color: #333;
            }

            p {
                font-size: 16px;
                margin-top: 20px;
                color: #333;
            
            }

            .options {
                display: flex;
                flex-direction: column; 
                flex-wrap: wrap; 
                gap: 5px;
            }

            .options div {
                display: flex;
                align-items: center;
            }

            label {
                margin-left: 5px;
                font-size: 14px;
                color: #333;
            }

            input[type="text"], input[type="radio"], input[type="checkbox"] {
                padding: 8px;
                margin-bottom: 10px;
                border: 1px solid #ccc;
                border-radius: 3px;
            }

            input[type="text"]:focus, input[type="radio"]:focus, input[type="checkbox"]:focus {
                outline: none;
                border-color: #007bff;
            }

            button {
                display: inline-block;
                padding: 6px 12px;
                margin-left: 0;
                font-size: 14px;
                line-height: 1.42857143;
                text-align: center;
                vertical-align: middle;
                touch-action: manipulation;
                color: #fff;
                border: 1px solid transparent;
                border-radius: 4px;
                user-select: none;
                cursor: pointer;
            }

            button:hover {
                background-color: #0056b3;
            }
     
            #result {
                text-align: center;
                font-size: 20px;
                font-weight: bold;
                margin-top: 20px;
            }

            #prev {
                background-color: #f0ad4e;
                border-color: #eea236;
                margin-left: 0;
                visibility: visible;
            }

            #next {
                background-color: #5cb85c;
                border-color: #4cae4c;
                margin-left: 0;
                visibility: visible;
            }

            #submit {
                background-color: #d9534f;
                border-color: #d43f3a;
                margin-left: 0;
            }

            #prev:hover {
                background-color: #eea236;
            }

            #next:hover {
                background-color: #4cae4c;
            }

            #submit:hover {
                background-color: #d43f3a;
            }

            #progress {
                font-size: 1rem;
                margin-top: 10px;
            }

            #report-container {
                display: none;
                margin-top: 20px;
                border: 1px solid #ccc;
                padding: 10px;
                background-color: #f9f9f9;
            }

            .question-report {
                margin: 20px 0;
                width: 100%;
                border: 1px solid #ccc;
                padding: 10px;
                background-color: #fff;
            }

            .correct-answer {
                background-color: #71ba5d;
                color: white;
            
            }

            .wrong-answer {
                background-color: #ff5e5e;
                color: white;
            }

            .not-answered {
                background-color: #fff;
                color: black;
            }

            #chart-container {
                margin-top: 20px;
                width: 100%;
                max-width: 600px; 
            }

            @media screen and (max-width: 600px) {
                p {
                    font-size: 15px; 
                }
                label {
                    font-size: 14px;
                }

                input[type="text"], input[type="radio"], input[type="checkbox"] {
                    width: 20px; 
                }
            }
        
            #question-index-container {
                margin-top: 20px;
                padding: 10px 30px 10px 30px;
                border: 1px solid #ccc;
                background-color: #f7f7f7;
                border-radius: 5px;
                display: flex; /* Use flexbox to display indices in a row */
                align-items: center; /* Center items vertically */
                flex-wrap: wrap; /* Wrap indices to the next row if needed */
            }

            #question-index-list {
                list-style-type: none;
                padding: 0;
                display: flex; /* Use flexbox to display indices in a row */
                flex-wrap: wrap; /* Wrap indices to the next row if needed */
            }

            #question-index-list li {
                cursor: pointer;
                width: auto;
                text-align: center;
                color: #fff;
                margin: 5px;
                padding: 5px;
                background-color: #0a0000;
                border-radius: 3px;
                transition: background-color 0.2s;
            }

            #question-index-list li:hover {
                background-color: #d0d0d0;
            }
            /* Brand tag background style */
            .brand-tag {
                position: absolute;
                top: 50%;
                left: 50%;
                transform: translate(-50%, -50%);
                opacity: 4.5;
                font-size: 20px;
                rotate: -30deg;
                color: #0e0c0c; /* Text color */
                /* Add any additional styles you want for the brand tag */
            }
            @media print{    
                .no-print, .no-print *{
                    display: none !important;
                }

                body {
    	            display: none !important;
    	            visibility: hidden !important;
                }
            }

            /* Add this CSS for the modal dialog */
            .modal {
             
                display: none;
                position: absolute;
                z-index: 1;
                left: 0;
                margin: 40px;
                top: 0;
                width: 100%;
                height: 100%;
                overflow: hidden;
                background-color: rgba(0,0,0,0.4);

            }

            .modal-content {
                position: fixed;
                top: 10%;
                left: 50%;
                transform: translate(-50%, -50%);
                background-color: #fefefe;
                margin: 15% auto;
                padding: 20px;
                border: 1px solid #888;
                width: 80%;
                max-width: 400px;
                height: 150px;
                text-align: center;
                border-radius: 5px;
                box-shadow: 0 4px 8px 0 rgba(0, 0, 0, 0.2);
            }

            /* Style the buttons */
            #confirmSubmit {
                background-color: #5bc0de;
                border-color: #46b8da;
                color: white;
                border: none;
                padding: 10px 20px;
                float: right;
                margin: 10px;
                cursor: pointer;
                border-radius: 5px;
            }
            #confirmSubmit:hover{
                background-color: #3fb5da;
            }
            #cancelSubmit {
                background-color: #d9534f;
                border-color: #d43f3a;
                color: white;
                border: none;
                padding: 10px 20px;
                float: left;
                margin: 10px;
                cursor: pointer;
                border-radius: 5px;
            }
            #cancelSubmit:hover{
                background-color: #d43f3a;
            }

            /* Add styles for the start page */
            #start-page {
                overflow: auto;
                height: 600px;
                margin-left: 30px;
                margin-bottom: 30px;
                padding: 20px;
                background-color: #fff;
                box-shadow: 0 10px 30px rgba(0 0 0 / 96%);
                border-radius: 5px;
            }

            #start-page h1 {
                font-size: 24px;
                color: #333;
            }

            #start-button {
                display: inline-block;
                padding: 12px 24px;
                font-size: 18px;
                background-color: #007bff;
                color: #fff;
                border: none;
                border-radius: 4px;
                cursor: pointer;
            }

            #start-button:hover {
                background-color: #0056b3;
            }

            /* Add styles to the score summary table */
            #score-summary {
                width: 95%;
                border-collapse: collapse;
                margin-top: 20px;
                margin-bottom: 20px;
            }

            #score-summary th {
                background-color: #f2f2f2;
                padding: 10px;
                text-align: center;
            }

            #score-summary td {
                padding: 10px;
                text-align: center;
            }

            #score-summary tbody tr:nth-child(odd) {
                background-color: #f9f9f9;
            }

            #score-summary tbody tr:hover {
                background-color: #e0e0e0;
            }

            /* Style individual cells */
            #user-score,
            #total-time-taken,
            #correct-answers,
            #wrong-answers,
            #unattempted {
                font-weight: bold;
                color: #007bff;
            }

            /* Style the "Calculating..." text */
            #user-score:empty::before,
            #total-time-taken:empty::before,
            #correct-answers:empty::before,
            #wrong-answers:empty::before,
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            &lt;h1&gt;&lt;img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhel7OImnB5XQaxW7H5kT2IS8avjb0CXrYYHaqkSR0qa7ENwkKnt4UycIW3vzONbOmfVmmJUYw6bno2rR9tzIDZFCt8df8TWgBwYK7quGM_4c0fjEjpWKJ8WWPMINLXjO-Ew4XCEQx9tgXjfhQ4B-KOc3IRFrWgx1YoCK0M6DAR7tNboYza8fdvjPg5Qok/s320/govind-Model.png" style="height: 60px; margin-top: 0px; width: 80px;" /&gt;AERO GATE TOPPER&lt;/h1&gt;
            &lt;h1&gt;Welcome to the Online Quiz&lt;/h1&gt;
            &lt;p&gt;In following Quiz total 20 basic questions of Basic Strength of Materials.&lt;/p&gt;
            &lt;p&gt;&lt;input disabled="" type="radio" /&gt;  Multiple Choice Question [MCQ]&lt;/p&gt;
            &lt;h4&gt;Instructions&lt;/h4&gt;
            &lt;p&gt;Your quiz data not recorded so if you refresh page then you lost your progress.&lt;/p&gt;
            &lt;p&gt;Your quiz report not permanent, if you refresh page then you lost your progress report.&lt;/p&gt;
            &lt;p&gt;1. In result if question shown in green background box it's mean your answer is correct&lt;/p&gt;
            &lt;p&gt;2. In result if question shown in red background box it's mean your answer is incorrect&lt;/p&gt;
            &lt;p&gt;3. In result if question shown in white background box it's mean you don't attempt that Question&lt;/p&gt;
            
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                &lt;div class="category-calculator"&gt;
                    &lt;div class="quiz-attempt-title" style="float: left;"&gt;
                        &lt;p&gt;GATE Aerospace Strength of Materials&lt;/p&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;div style="clear: both;"&gt;&lt;/div&gt;
                &lt;div id="timer" style="display: block; float: right; font-size: 13px; font-weight: bold;"&gt;Time Left: 35:00&lt;/div&gt;
       
                &lt;hr /&gt;
                &lt;!-- Question 1 --&gt;
                &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                
                        &lt;span class="question-marks" style="margin-right: 10px;"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;1. For a simply supporting beam on two end supports the Bending Moment is maximum&lt;/p&gt;
                    
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options1" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Usually on the supports&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options1" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Always at mid span&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options1" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Where there is no shear force&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options1" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Where the deflection is maximum
&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 2 --&gt;
                &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;2. A concentrated load P acts on a simply supported beam of span L at a distance L/3 from the left support. The bending moment at the point of application of the load is given by&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options2" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;PL/3&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options2" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;2PL/3&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options2" type="radio" value="c" /&gt;
                            &lt;label for="mcq-option3"&gt;PL/9&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options2" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;2PL/9&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 3 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;3. The beams, one having square cross section and another circular cross-section, are subjected to the same amount of bending moment. If the cross-sectional area as well as the material of both the beams are the same then&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options3" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Maximum bending stress developed in
both the beams is the same&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options3" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;The circular beam experience more
bending stress than the square one&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options3" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;The square beam experience more bending
stress than the circular one&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options3" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;As the material is same both beams will
experience same deformation&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 4 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="2" data-incorrect-score="-0.67" data-question-score="2" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;4.  A simply supported beam of length L is subjected to a varying distributed load sin(3π x/L)Nm&lt;sup&gt;-1&lt;/sup&gt; , where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options4" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt; Zero&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options4" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;L/3π&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options4" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;L/π&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options4" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;2L/π&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 5 --&gt;
                &lt;div class="question" data-answer="D" data-correct-score="2" data-incorrect-score="-0.67" data-question-score="2" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;5. Consider a simply supported beam of length 50h, with a rectangular cross-section of depth h, and width 2h. The beam carries a vertical point load P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beams is&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options5" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;0.02&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options5" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;0.10&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options5" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;0.05&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options5" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;0.01&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 6 --&gt;
                &lt;div class="question" data-answer="A" data-correct-score="2" data-incorrect-score="-0.67" data-question-score="2" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;2&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.67&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;6. The shear stress at the neutral axis in a beam of triangular section with at base of 40 mm and height 20 mm, subjected to a shear force of 3 kN is&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options6" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;3 MPa&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options6" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;6 MPa&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options6" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;10 MPa&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options6" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;20 MPa&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 7 --&gt;
                &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;7. A cantilever beam curved in plane is subjected to lateral loads will develop at any section&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options7" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Bending moment and shearing force&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options7" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Bending moment and twisting moment&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options7" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Twisting moment and shearing force&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options7" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Bending moment, twisting moment and
shearing force&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 8 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;8. For a given shear force across a symmetrical ‘I’ section, the intensity of shear stress is maximum at the&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options8" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Extreme fibres&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options8" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Centroid of the section&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options8" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;At the junction of the flange and the web, but on the web&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options8" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;At the junction of the flange and the web, but on the flange&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 9 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;9. If the shear force at a section of beam under bending is equal to zero then the bending moment at the section is&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options9" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Zero&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options9" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Constant&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options9" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Maximum&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options9" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Minimum&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 10 --&gt;
                &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;10. Two people weighing W each are sitting on a plank of length L floating on water at L/4 from either end Neglecting the weight of the plank, the bending moment at the centre of the plank is&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options10" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Zero&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options10" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;WL/32&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options10" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;WL/16&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options10" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;WL/8&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 11 --&gt;
                &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;11. The following statement are related to bending of beams&lt;/p&gt;
                  &lt;p&gt; I. The slope of the bending moment diagram is equal to the shear force.&lt;/p&gt;
                  &lt;p&gt; II. The slope of the shear force diagram is equal to the load intensity. &lt;/p&gt;
                  &lt;p&gt; III. The slope of the curvature is equal to the flexural rotation.&lt;/p&gt;
                  &lt;p&gt; IV. The second derivative of the deflection is equal to the curvature.&lt;/p&gt;
                  &lt;p&gt; The only FALSE statement is &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options11" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;I&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options11" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;II&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options11" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;III&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options11" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;IV&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 12 --&gt;
                &lt;div class="question" data-answer="A" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;12. The “Plane section remain plane” assumption in bending theory implies&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options12" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Strain profile is linear&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options12" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Stress profile is linear&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options12" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Both profiles are linear&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options12" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Shear deformation is neglected&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 13 --&gt;
                &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                  &lt;p&gt;13. Consider the following statements:&lt;/p&gt;
&lt;p&gt;If a section at a distance from one of the ends of the beam, M represents the bending moment, the shear force and w the intensity of loading, then&lt;/p&gt;
                  &lt;p&gt; 1. dM/ dx = V&lt;/p&gt;
                  &lt;p&gt;2. dV/dx = w&lt;/p&gt;
                  &lt;p&gt;3. dw/dx = y (the deflection of the beam at the section)&lt;/p&gt;
                  &lt;p&gt;Which of these statements are correct?&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options13" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;1,2 and 3&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options13" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;2 and 3&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options13" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;1 and 3&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options13" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;1 and 2&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 14 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;14. If a beam is subjected to a constant bending moment along its length, then the shear force will&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options14" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Also have a constant value everywhere along its length&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options14" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Be zero at all sections along the beam&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options14" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Be maximum at the centre and maximum at the ends&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options14" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Zero at the centre and maximum at the ends&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 15 --&gt;
                &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;15. Two beams of equal cross-sectional area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, then &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options15" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Both beams will be equally strong&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options15" type="radio" value="0.30" /&gt;
                            &lt;label for="mcq-option2"&gt;Circular section beam will be stronger&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options15" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Square section beam will be stronger&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options15" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;The strength of the beam will depends on the nature of loading&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 16 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                  &lt;p&gt;16.  Consider the following statements in case of beams: &lt;/p&gt;
                  &lt;p&gt; 1. Rate of change of shear force is equal to the rate of loading at a particular section &lt;/p&gt;
                  &lt;p&gt; 2. Rate of change of bending moment is equal to the shear force at a particular section&lt;/p&gt;
&lt;p&gt; 3. Maximum shear force in a beam occurs at a point where bending moment is either zero or bending moment changes sign&lt;/p&gt;
                  &lt;p&gt; Which of the above, statements are correct?&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options16" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;1,2 and 3&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options16" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;1 and 2&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options16" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;1 alone&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options16" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;2 alone&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 17 --&gt;
                &lt;div class="question" data-answer="C" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;17. A simply supported beam has equal overhanging lengths and carries equal concentrated loads P at ends. Bending moment over the length between the supports&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options17" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Is zero&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options17" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;. Is maximum at mid-span&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options17" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Is a non-zero constant&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options17" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Varies uniformly from one support to the other&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 18 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;18. What is the nature of distribution of shear
stress in a rectangular beam? &lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options18" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Linear&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options18" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt; Parabolic&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options18" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Hyperbolic&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options18" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Elliptic&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 19 --&gt;
                &lt;div class="question" data-answer="B" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                    &lt;/div&gt;
                    &lt;p&gt;19. The point of contra flexure is a point where:&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options19" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;Shear force changes sign&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options19" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt;Bending moment changes sign&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options19" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt;Shear force is maximum&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options19" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt;Bending moment is maximum&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;
                &lt;!-- Question 20 --&gt;
                &lt;div class="question" data-answer="D" data-correct-score="1" data-incorrect-score="-0.33" data-question-score="1" data-type="MCQ"&gt;
                    &lt;div class="question-info"&gt;
                        &lt;span class="question-type"&gt;Question Type: &lt;b&gt;Multiple Choice Question&lt;/b&gt;&lt;/span&gt;
                        &lt;div&gt;&lt;br /&gt;&lt;/div&gt;
                        &lt;span class="question-marks"&gt;
                            Marks for correct answer: &lt;span style="color: green;"&gt;1&lt;/span&gt; |
                            Nagative Marks: &lt;span style="color: red;"&gt;0.33&lt;/span&gt;
                        &lt;/span&gt;
                
                    &lt;/div&gt;
                    &lt;p&gt;20. In the case of beams with circular cross
section, what is the ratio of the maximum
shear stress to average shear stress?&lt;/p&gt;
                    &lt;div class="options"&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option1" name="mcq-options20" type="radio" value="A" /&gt;
                            &lt;label for="mcq-option1"&gt;3:1&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option2" name="mcq-options20" type="radio" value="B" /&gt;
                            &lt;label for="mcq-option2"&gt; 2:1&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option3" name="mcq-options20" type="radio" value="C" /&gt;
                            &lt;label for="mcq-option3"&gt; 3:2&lt;/label&gt;
                        &lt;/div&gt;
                        &lt;div&gt;
                            &lt;input id="mcq-option4" name="mcq-options20" type="radio" value="D" /&gt;
                            &lt;label for="mcq-option4"&gt; 4:3&lt;/label&gt;
                        &lt;/div&gt;
                    &lt;/div&gt;
                &lt;/div&gt;

    
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                &lt;button id="next"&gt;Save &amp;amp; Next&lt;/button&gt;
                &lt;button id="submit"&gt;Submit&lt;/button&gt;
                &lt;!-- &lt;button class="btn-sm btn-info" id="calc-btn" onClick="$('#calc').window('open');"&gt;&lt;img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirV3i0cTNot3yoHR1h9JSYpcw6XvXFE8_k_lWqrJc3In8C0QBsDD29cbmgckiV_JqwyA63f4fYGMu-gUk2pXRCG8wB7DWPD8mOFhlmU6Iaj2pSz7nTx8SI7ROAx6GLMvpDJpCH9N37lnAKJylJDXsmz6946S6qwTBIy8OCydd_ZRYUyk8whSWgK4mIwg/s1600/calc.png" alt="calc" height="20"&gt; Calculator &lt;/button&gt; --&gt;

                

            &lt;/div&gt;
      &lt;/div&gt;
        &lt;div id="warning-popup" style="display: none;"&gt;
              &lt;p&gt;This is the last question. Are you sure you want to proceed?&lt;/p&gt;
              &lt;button id="confirm-warning"&gt;Yes&lt;/button&gt;
              &lt;button id="cancel-warning"&gt;No&lt;/button&gt;
        &lt;/div&gt;
  
        &lt;!-- Calculator container (initially hidden) --&gt;
        &lt;div id="calc-container" style="display: none;"&gt;
              &lt;div class="panel window window-thinborder c6 panel-htop" style="width: 480px;"&gt;
                  &lt;div class="panel-header panel-header-noborder window-header" style="width: 478px;"&gt;
                      &lt;div class="panel-icon icon-sum"&gt;&lt;/div&gt;
                      &lt;div class="panel-tool"&gt;
                          &lt;a class="panel-tool-collapse" href="javascript:;"&gt;&lt;/a&gt;
                          &lt;a class="panel-tool-close" href="javascript:;"&gt;&lt;/a&gt;
                      &lt;/div&gt;
                  &lt;/div&gt;
                  &lt;div class="easyui-window panel-body panel-body-noborder window-body" data-options="iconCls:'icon-sum',minimizable:false,maximizable:false,resizable:false,border:'thin',cls:'c6',closed:true" id="calc" style="height: 300px; width: 478px;" title=""&gt;
                      &lt;!-- Replace the URL with your calculator URL or embed code --&gt;
                      &lt;iframe frameborder="0" height="300px" scrolling="no" src="https://shorturl.at/htFOS" width="475px"&gt;
                      &lt;/iframe&gt;
                  &lt;/div&gt;
              &lt;/div&gt;
        &lt;/div&gt;
  
        &lt;!-- Result section (initially hidden) --&gt;
        &lt;div id="result-container" style="display: none;"&gt;
              &lt;!-- Your result display code (remains the same) --&gt;
              &lt;div id="result"&gt;&lt;/div&gt;
  
              &lt;!-- Display user's score summary in a table --&gt;
              &lt;table id="score-summary"&gt;
                  &lt;thead&gt;
                      &lt;tr&gt;
                          &lt;th style="background: #337ab7; color: white;"&gt;Quiz Name&lt;/th&gt;
                          &lt;th style="background: #337ab7; color: white;"&gt;Score&lt;/th&gt;
                          &lt;th style="background: #337ab7; color: white;"&gt;Time Spend (Approx.)&lt;/th&gt;
                          &lt;th style="background: #337ab7; color: white;"&gt;Correct&lt;/th&gt;
                          &lt;th style="background: #337ab7; color: white;"&gt;Incorrect&lt;/th&gt;
                          &lt;th style="background: #337ab7; color: white;"&gt;Unattempted&lt;/th&gt;
                      &lt;/tr&gt;
                  &lt;/thead&gt;
                  &lt;tbody&gt;
                      &lt;tr&gt;
                          &lt;td style="font-weight: bold;"&gt;Strengh of Material - Stress in Beam&lt;/td&gt;
                          &lt;td id="user-score"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="total-time-taken"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="correct-answers"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="wrong-answers"&gt;Calculating...&lt;/td&gt;
                          &lt;td id="unattempted"&gt;Calculating...&lt;/td&gt;
                      &lt;/tr&gt;
                  &lt;/tbody&gt;
              &lt;/table&gt;
  
  
              &lt;!-- Canvas for the chart --&gt;
              &lt;canvas height="200" id="resultChart" width="400"&gt;&lt;/canvas&gt;
        &lt;/div&gt;
  
        &lt;!-- Report section (initially hidden) --&gt;
        &lt;div id="report-container"&gt;
              &lt;!-- The report will be displayed here --&gt;
  
        &lt;/div&gt;

        &lt;script&gt;
        
            // Define quiz-related variables and constants
            let currentQuestion = 0;
            let questions = document.getElementsByClassName('question');
            let resultHTML = '';
            let timerInterval=0;
            const countdownMinutes = 31;
            let countdownSeconds = countdownMinutes * 60;
            const timeTakenArray = Array.from(questions).map(() =&gt; 0); // Array to store time taken for each question
            const questionStartTimes = Array.from(questions).map(() =&gt; 0);
            const StartTime=0;
        


            // Get references to the calculator button and container
           // const calcBtn = document.getElementById('calc-btn');
           // const calcContainer = document.getElementById('calc-container');

            // Add a click event listener to the calculator button
           // calcBtn.addEventListener('click', function () {
                // Toggle the display of the calculator container
             //   if (calcContainer.style.display === 'none' || calcContainer.style.display === '') {
               //     calcContainer.style.display = 'block';
              //  } else {
              //      calcContainer.style.display = 'none';
            //    }
            //});

            
            document.getElementById('start-button').addEventListener('click', function () {
                // Hide the start page and show the quiz container
                document.getElementById('start-page').style.display = 'none';
                document.getElementById('container').style.display = 'block';
                document.getElementById('quiz-container').style.display = 'block';
                document.getElementById('footer_buttons').style.display = 'block';

                // Load the first question to start the quiz
                loadQuestion(0);                    
                // Start the countdown timer
                startCountdown();
            });
            
        
            // Update the question index list click event listener to use loadQuestion
            function generateQuestionIndices() {
             const questionIndexList = document.getElementById('question-index-list');

                 for (let i = 0; i &lt; questions.length; i++) {
                      const listItem = document.createElement('li');
                     listItem.textContent = `${i + 1}`;

                        // Add click event listener to load the question by index
                     listItem.addEventListener('click', () =&gt; loadQuestion(i));

                     questionIndexList.appendChild(listItem);
                 }
        }
            // Call the function to generate question indices
            generateQuestionIndices();
        
            // Function to update the timer display
            function updateTimerDisplay() {
            const minutes = Math.floor(countdownSeconds / 60);
            const seconds = countdownSeconds % 60;
            const formattedTime = `${minutes.toString().padStart(2, '0')}:${seconds.toString().padStart(2, '0')}`;
            document.getElementById('timer').textContent = `Time Left: ${formattedTime}`;
}

            // Function to handle the timer countdown
            function startCountdown() {
                updateTimerDisplay();
                timerInterval = setInterval(() =&gt; {
                    countdownSeconds--;
                    if (countdownSeconds &lt; 0) {
                        clearInterval(timerInterval);
                        document.getElementById('timer').textContent = "Time's Up!";
                        showResult();
                    } else {
                        updateTimerDisplay();
                    }
                }, 1000);
            }
            
            // Function to record the time taken for the current question
            function recordTimeTaken() {
                const questionEndTime = Date.now();
                const questionStartTime = questionStartTimes[currentQuestion];
                const timeTaken = ((questionEndTime - questionStartTime) / 1000).toFixed(2); // Calculate time taken in seconds
                // Calculate cumulative time taken for the current question
                timeTakenArray[currentQuestion] = (timeTakenArray[currentQuestion] || 0) + parseFloat(timeTaken);
                // Update the start time for the current question
                questionStartTimes[currentQuestion] = questionEndTime;
            }

            // Function to load a question
            function loadQuestion(questionIndex) {
                for (let i = 0; i &lt; questions.length; i++) {
                    questions[i].style.display = 'none';
                }
                
                if (questionIndex &gt;= 0 &amp;&amp; questionIndex &lt; questions.length) {
                    currentQuestion = questionIndex;
                    questions[currentQuestion].style.display = 'block';
                
                    // Record the start time of the question if it's not set yet
                    if (!questionStartTimes[currentQuestion]) {
                        questionStartTimes[currentQuestion] = Date.now();
                    }
                
                    // Update the chart when loading a question
                    updateChart();
                
                    // Show the current question and hide the "Previous" and "Next" buttons as needed
                    showQuestion(currentQuestion);
                }
            }
            loadQuestion(0);

            function showQuestion(index) {
                for (var i = 0; i &lt; questions.length; i++) {
                    questions[i].style.display = i === index ? "block" : "none";
                }
                document.getElementById("prev").style.display = index === 0 ? "none" : "inline";
                document.getElementById("next").style.display = index === questions.length - 1 ? "none" : "inline";
            }


            // Add this function to show the warning popup
            function showWarningPopup() {
                const warningPopup = document.getElementById('warning-popup');
                warningPopup.style.display = 'block';

                // Handle the "Yes" button click inside the warning popup
                document.getElementById('confirm-warning').addEventListener('click', function () {
                    warningPopup.style.display = 'none';
            
                });

                // Handle the "No" button click inside the warning popup
                document.getElementById('cancel-warning').addEventListener('click', function () {
                    warningPopup.style.display = 'none';
                });
            }

            // Function to handle the "Previous" button click
            function prevQuestion() {
                recordTimeTaken();
                currentQuestion--;
                // Reset start time for new current question
                questionStartTimes[currentQuestion] = Date.now();
                showQuestion(currentQuestion);
                console.log(`Total time spent on this question: ${timeTakenArray[currentQuestion]} seconds`);
              
              
                // Enter fullscreen for the quiz container
                const quizContainer = document.getElementById('container');
                quizContainer.requestFullscreen();
                    
            }

            // Function to handle the "Next" button click
            function nextQuestion() {
                recordTimeTaken();
                currentQuestion++;
                // Reset start time for new current question
                questionStartTimes[currentQuestion] = Date.now();
                showQuestion(currentQuestion);
                console.log(`Total time spent on this question: ${timeTakenArray[currentQuestion]} seconds`);
              
              
                // Enter fullscreen for the quiz container
                const quizContainer = document.getElementById('container');
                quizContainer.requestFullscreen();
                
            }


            // Function to handle submitting the quiz
            function submitQuiz() {
                recordTimeTaken(); // Record time taken for the last question

                // Display the modal dialog when submitting the quiz
                const modal = document.getElementById('myModal');
                modal.style.display = 'block';

                // Handle the "Yes" button click inside the modal
                document.getElementById('confirmSubmit').addEventListener('click', function() {
                    clearInterval(timerInterval); // Stop the timer only when submitting
                    modal.style.display = 'none';
                    showResult();
                });

                // Handle the "No" button click inside the modal
                document.getElementById('cancelSubmit').addEventListener('click', function() {
                    modal.style.display = 'none';
                  
                  
                // Enter fullscreen for the quiz container
                const quizContainer = document.getElementById('container');
                quizContainer.requestFullscreen();
                });

                // Exit fullscreen after submitting the quiz
        const doc = window.document;
        const exitFullScreen = doc.exitFullscreen || doc.mozCancelFullScreen || doc.webkitExitFullscreen || doc.msExitFullscreen;
        exitFullScreen.call(doc);
            }

            // Function record user's score
            function calculateScore() {
                let userTotalScore = 0;
                let totalPossibleScore = 0; // Initialize the total possible score

                // Get all question elements with the class "question"
                const questions = document.getElementsByClassName('question');

                // Iterate through each question
                for (let i = 0; i &lt; questions.length; i++) {
                    const question = questions[i];
        
                    // Get the user's selected options (radio buttons or checkboxes)
                    const selectedOptions = Array.from(question.querySelectorAll('input:checked')).map(input =&gt; input.value).sort().join(';');

                    // Get the correct answer(s) from the "data-answer" attribute
                    const correctAnswer = question.getAttribute('data-answer').split(';').sort().join(';');

                    // Get the scoring values
                    const correctScore = parseFloat(question.getAttribute('data-correct-score'));
                    const incorrectScore = parseFloat(question.getAttribute('data-incorrect-score'));
                    const questionScore = parseFloat(question.getAttribute('data-question-score')); // Get the question score

                    // Calculate the question score
                    let score = 0;
                    if (selectedOptions === correctAnswer) {
                        // User's answer is correct
                        score = correctScore;
                    } else if (selectedOptions !== '' &amp;&amp; selectedOptions !== correctAnswer) {
                        // User attempted the question but got it wrong
                        score = incorrectScore;
                    } else {
                        // User did not attempt the question
                        score = 0;
                    }

                    // Add the calculated score to the user's total score
                    userTotalScore += score;

                    // Add the question score to the total possible score
                    totalPossibleScore += questionScore;
                }

                return { userTotalScore, totalPossibleScore };
            }
        

            // Function to display the result and report
            function showResult() {
                // Hide the quiz container and show the result and report containers
                document.getElementById('container').style.display = 'none';
                document.getElementById('quiz-container').style.display = 'none';
                document.getElementById('footer_buttons').style.display = 'none';
                document.getElementById('result-container').style.display = 'block';
                document.getElementById('report-container').style.display = 'block';

                // Initialize variables for tracking correct, wrong, and unattempted questions
                let correctAnswers = 0;
                let wrongAnswers = 0;
                let unattempted = 0;
                let totalScore = 0;

                // Calculate user's score and update counts for correct, wrong, and unattempted questions
                for (let i = 0; i &lt; questions.length; i++) {
                    const question = questions[i];
                    const correctAnswer = question.getAttribute('data-answer').split(';');
                    const selectedOptions = Array.from(question.querySelectorAll('input:checked')).map(input =&gt; input.value);
                    const userAnswer = selectedOptions.join(';');

                    if (userAnswer === correctAnswer.join(';')) {
                        correctAnswers++;
                        totalScore += parseFloat(question.getAttribute('data-correct-score'));
                    } else if (userAnswer !== '' &amp;&amp; userAnswer !== correctAnswer.join(';')) {
                        wrongAnswers++;
                        totalScore += parseFloat(question.getAttribute('data-incorrect-score'));
                    } else {
                        unattempted++;
                    }

                }
                // Calculate total time taken
                const totalSeconds = timeTakenArray.reduce((acc, time) =&gt; acc + parseFloat(time), 0);
                const totalMinutes = Math.floor(totalSeconds / 60);
                const remainingSeconds = Math.round(totalSeconds % 60); // Round the remaining seconds to the nearest whole number
                const totalTimeTaken = `${totalMinutes} min ${remainingSeconds} sec`;

                // Update the table with the calculated values
                document.getElementById('user-score').textContent = totalScore.toFixed(2);
                document.getElementById('total-time-taken').textContent = totalTimeTaken;
                document.getElementById('correct-answers').textContent = correctAnswers;
                document.getElementById('wrong-answers').textContent = wrongAnswers;
                document.getElementById('unattempted').textContent = unattempted;


                // Initialize the resultHTML variable to store the report HTML
                let resultHTML = '';

                // Loop through questions to generate the report
                for (let i = 0; i &lt; questions.length; i++) {
                    const question = questions[i];
                    const correctAnswer = question.getAttribute('data-answer').split(';');
                    const selectedOptions = Array.from(question.querySelectorAll('input:checked')).map(input =&gt; input.value);
                    const userAnswer = selectedOptions.join(';');

                    // Determine the class to apply for background color based on the user's answer
                    const backgroundClass = userAnswer === correctAnswer.join(';') ? 'correct-answer' : userAnswer === '' ? 'not-answered' : 'wrong-answer';

                    // Generate HTML for each question in the report
                    // Generate HTML for the report, including symbols
                    const resultSymbol = userAnswer === '' ? '❓' : userAnswer === correctAnswer.join(';') ? '✅' : '❌';

                    // Function to convert special characters to subscripts and superscripts
                    function convertSpecialCharsToHTML(text) {
                        return text
                        .replace(/&lt;sub&gt;/g, '_')
                        .replace(/&lt;sup&gt;/g, '^')
                        .replace(/_/g, '&lt;sub&gt;_&lt;/sub&gt;')
                        .replace(/\^/g, '&lt;sup&gt;^&lt;/sup&gt;');
                    }

                    const questionHTML = `
                        &lt;div class="question-report ${backgroundClass}"&gt;
                            &lt;div class="question-container ${backgroundClass}"&gt;
                                &lt;p&gt;Question Type: &lt;b&gt;${question.getAttribute('data-type')}&lt;/b&gt;&lt;/p&gt;
                                &lt;p&gt;
                                    Marks for correct answer:&amp;nbsp; &lt;span style="color: green"&gt;${question.getAttribute('data-correct-score')}&lt;/span&gt; 
                                    &amp;nbsp; | &amp;nbsp; 
                                    Negative Marks&amp;nbsp; &lt;span style="color: red"&gt;${question.getAttribute('data-incorrect-score')}&lt;/span&gt;
                                &lt;/p&gt;

                                &lt;p&gt;Question ${i + 1}&lt;/p&gt;
                                &lt;p&gt;${convertSpecialCharsToHTML(question.querySelector('p').innerHTML)}&lt;/p&gt;
                                &lt;p&gt;
                                &lt;div class="options"&gt;
                                    ${generateOptionsHTML(question)}
                                &lt;/div&gt;
                                &lt;/p&gt;
                                &lt;p&gt;&lt;strong&gt;Your Answer:&lt;/strong&gt; ${convertSpecialCharsToHTML(userAnswer || 'Not answered')}&lt;/p&gt;
                                &lt;p&gt;&lt;strong&gt;Correct Answer:&lt;/strong&gt; ${convertSpecialCharsToHTML(correctAnswer.join(';'))}&lt;/p&gt;
                                &lt;p&gt;&lt;strong&gt;Result:&lt;/strong&gt; ${resultSymbol} ${userAnswer === '' ? 'Not attempted' : userAnswer === correctAnswer.join(';') ? 'Correct' : 'Wrong'}&lt;/p&gt;
                            &lt;/div&gt;
                        &lt;/div&gt;
                    `;

                    resultHTML += questionHTML;
                }

                // Display the report in the report container
                document.getElementById('report-container').innerHTML = resultHTML;

                // Display the user's score
                const { userTotalScore, totalPossibleScore } = calculateScore();
                const userScoreText = `Your Score: ${userTotalScore.toFixed(2)} out of ${totalPossibleScore.toFixed(2)}`;
                document.getElementById('result').textContent = userScoreText;

                // Call the updateChart function to display the chart (assuming you have an updateChart function)
                updateChart();
            }


            // Function to generate HTML for options
            function generateOptionsHTML(question) {
                const optionsHTML = [];
                const options = question.querySelectorAll('input[type="radio"], input[type="checkbox"]');

                options.forEach((option) =&gt; {
                    const label = option.nextElementSibling;
                    optionsHTML.push(`
                        &lt;div&gt;
                            &lt;input type="${option.type}" value="${option.value}" ${option.checked ? 'checked' : ''} disabled&gt;
                            &lt;label&gt;${label.textContent}&lt;/label&gt;
                        &lt;/div&gt;
                    `);
                });

                return optionsHTML.join('');
            }

            // Event listeners for navigation buttons
            document.getElementById('prev').addEventListener('click', prevQuestion);
            document.getElementById('next').addEventListener('click', nextQuestion);
            document.getElementById('submit').addEventListener('click', submitQuiz);

            // Start the countdown timer when the page loads
            startCountdown();

            // Load the first question
            loadQuestion(0);

            // Show a warning when the user tries to leave the page (e.g., by refreshing)
            window.addEventListener('beforeunload', function (e) {
                e.preventDefault();
                e.returnValue = 'You have unsaved changes. Are you sure you want to leave?';
            });

            // Calculator Button Click Event
            document.getElementById('calculator').addEventListener('click', function () {
                // Implement calculator functionality here
                alert('Open Calculator');
            });

            // Function to update the chart
            function updateChart() {
                const ctx = document.getElementById('resultChart').getContext('2d');
                // Create a chart using Chart.js
                const chart = new Chart(ctx, {
                    type: 'bar',
                    data: {
                        labels: timeTakenArray.map((_, index) =&gt; `Q ${index + 1}`),
                        datasets: [{
                            label: 'Time Taken (seconds)',
                            data: timeTakenArray,
                            backgroundColor: 'rgba(0, 123, 255, 0.7)',
                        }]
                    },
                    options: {
                        scales: {
                            y: {
                                beginAtZero: true,
                                title: {
                                    display: true,
                                    text: 'Time Spend (seconds)'
                                }
                            },
                            x: {
                                title: {
                                    display: true,
                                    text: 'Question Number'
                                }
                            }
                        },
                    }
                });
            }   
        &lt;/script&gt;
    &lt;/body&gt;
&lt;/html&gt;

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&lt;/script&gt;</description><link>https://aerogatetopper.blogspot.com/2023/12/stress-in-beams.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhel7OImnB5XQaxW7H5kT2IS8avjb0CXrYYHaqkSR0qa7ENwkKnt4UycIW3vzONbOmfVmmJUYw6bno2rR9tzIDZFCt8df8TWgBwYK7quGM_4c0fjEjpWKJ8WWPMINLXjO-Ew4XCEQx9tgXjfhQ4B-KOc3IRFrWgx1YoCK0M6DAR7tNboYza8fdvjPg5Qok/s72-c/govind-Model.png" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-1870151006310400420</guid><pubDate>Mon, 29 May 2023 16:30:00 +0000</pubDate><atom:updated>2023-12-17T10:53:38.183+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">INTERVIEW</category><title>DRDO Interview Questions for Aerospace Engineering Part- 2</title><description>&lt;h3 style="text-align: center;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;DRDO INTERVIEW QUESTIONS FOR AEROSPACE ENGINEERING&lt;/span&gt;&lt;/h3&gt;&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Hello everyone! Welcome to our blog,
where I'll be sharing valuable insights about interview questions related to
Aerospace Engineering in DRDO (Defense Research and Development Organization).
If you have aspirations to work in defense research and development, cracking a
DRDO interview is a significant achievement. In this article, I'll provide you
with essential information about DRDO interviews and offer some interview
questions to assist you during your interview. Let's get started!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEtnz9W5t_SaumQzdOvBSw_iB-w09ttI2aRjgo8enOg69j1E81m67BZJKeIGzWGYNOMIKvc75P8c74EER5qpn7x4jgirSIYmn51XU4wm7Lmm4__isEPet-jHLMKOWFuyBaRDMSNfYaOtrjERgPbj05a5dRm0qWh4OoGsAWhU34X6xtd5wrhBklGF-VDA/s584/Aero%20GATE%20Topper.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;img border="0" data-original-height="328" data-original-width="584" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEtnz9W5t_SaumQzdOvBSw_iB-w09ttI2aRjgo8enOg69j1E81m67BZJKeIGzWGYNOMIKvc75P8c74EER5qpn7x4jgirSIYmn51XU4wm7Lmm4__isEPet-jHLMKOWFuyBaRDMSNfYaOtrjERgPbj05a5dRm0qWh4OoGsAWhU34X6xtd5wrhBklGF-VDA/s16000/Aero%20GATE%20Topper.jpg" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;br /&gt;&lt;p align="center" class="MsoNormal" style="text-align: center;"&gt;&lt;br /&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; In this article, I have included a
selection of questions and provided details about the interview process. If you
choose not to pursue a Master's degree after GATE, the questions will focus on
your bachelor's subject, area of interest, and your B.Tech project &amp;amp;
seminar. However, if you pursue a Master's degree after GATE, the questions
will revolve around your specialization. For those in their final year or who
have completed their final year, they will mainly inquire about your MTP (Major
Technical Project), covering various aspects of your project.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

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&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; During the interview, they typically
don't ask direct questions about your project but assess your understanding of
the project's concepts. Additionally, many questions are application-based and
relate to your project.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

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&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &lt;b&gt;&lt;span style="font-size: medium;"&gt;&amp;nbsp;DRDO INTERVIEW QUESTION:- &lt;/span&gt;&lt;a href="https://aerogatetopper.blogspot.com/2023/05/DRDO-interview-questions-for-Aerospace-Structure.html" target="_blank"&gt;Read More Click Here&lt;/a&gt;&lt;/b&gt;&lt;/span&gt;&lt;/p&gt;
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&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;For those who have transitioned from
Aerospace to a different department during their Master's, here are some other
questions they may encounter.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;1.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;1. How thick is the shock wave?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;2.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;2. Can you provide the Cl versus alpha
curve for both thin and thick airfoils?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;3.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;3. What are the advantages and
disadvantages of thin and thick airfoils?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;4.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;4. How far apart is the bow shock from
the object?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;5.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;5. Could you explain reflective shock
waves?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;

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&lt;p class="MsoListParagraphCxSpMiddle" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;6.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;6. If we analyze the path of a
particle associated with a cylindrical body in 2D for different Reynolds
numbers, what type of path does the particle follow? Can you illustrate it?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;7.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;7. What is the definition of degree of
freedom, and how can it be explained?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;8.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;8. Could you clarify the concept of
mode shape?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;9.&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;9. What does Lambda (λ) represent in
the spring-mass equation?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;10&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;10. What is the physical meaning or
significance of Lambda (λ)?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;11&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;; font-feature-settings: normal; font-kerning: auto; font-optical-sizing: auto; font-size: 7pt; font-stretch: normal; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variation-settings: normal; line-height: normal;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;11. Can you explain the physical
interpretation of eigenvalues and eigenvectors?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-align: justify; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;12&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;12. Draw the stress-strain curve for
steel and aluminum?&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoListParagraphCxSpMiddle" style="text-align: justify;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;

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</description><link>https://aerogatetopper.blogspot.com/2023/05/drdo-interview-questions-for-aerospace-engineering-part-2.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEtnz9W5t_SaumQzdOvBSw_iB-w09ttI2aRjgo8enOg69j1E81m67BZJKeIGzWGYNOMIKvc75P8c74EER5qpn7x4jgirSIYmn51XU4wm7Lmm4__isEPet-jHLMKOWFuyBaRDMSNfYaOtrjERgPbj05a5dRm0qWh4OoGsAWhU34X6xtd5wrhBklGF-VDA/s72-c/Aero%20GATE%20Topper.jpg" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-2770910835741701163</guid><pubDate>Sun, 21 May 2023 08:37:00 +0000</pubDate><atom:updated>2023-05-29T19:22:27.806+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">INTERVIEW</category><title>DRDO interview questions for Aerospace Structure</title><description>&lt;h3 style="text-align: center;"&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,serif;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;DRDO INTERVIEW QUESTIONS FOR AEROSPACE ENGINEERING&lt;/span&gt;&lt;/h3&gt;

&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Hello everyone, Welcome to our blog, where today I'll be
sharing valuable insights about &lt;/span&gt;&lt;b&gt;DRDO
(Defense Research and Development Organization) interview questions for
Aerospace Structure.&lt;/b&gt;&lt;span style="font-weight: normal;"&gt; If you aspire to work in the field of defense research
and development, cracking a DRDO interview is a significant milestone. In this
article, I'll provide you with essential information about DRDO interviews and
present some interview questions to help you in your interview. Let's dive in!&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;img border="0" class="placeholder" id="b6a64c4163532" src="https://blogger.googleusercontent.com/img/a/AVvXsEibPtM_9eB891iH90RGRSO9Fq9sxmwsKR-9PTi95AIqBsPrDMAXoxSTUkIvry5l9XOYGB1Z8YglFHFyQ3tKAj8IhJFLKw7m9kTKAM3dTaCF9DUKoJTDGtI7SlJ06XMGTm6V6lYPJlKUug962r-fS2HJtVOOvUjqx9Yfd15qOl9YiwT_1wxeTjzMprvWmQ=s16000" style="background-color: #d8d8d8; background-image: url('https://fonts.gstatic.com/s/i/materialiconsextended/insert_photo/v6/grey600-24dp/1x/baseline_insert_photo_grey600_24dp.png'); background-position: 50% 50%; background-repeat: no-repeat; opacity: 0.6;" /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;br /&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;p&gt;&lt;/p&gt;

&lt;h4 style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: left; white-space: pre-wrap;"&gt;&lt;b&gt;&lt;span style="font-family: arial;"&gt;Introduction to DRDO interview&lt;/span&gt;&lt;/b&gt;&lt;/h4&gt;

&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; DRDO interviews are rigorous and aim to evaluate candidates'
technical knowledge, problem-solving abilities, and their suitability for
research and development roles within the organization. The interview panel
generally consists of five-seven experts from various defense technology domains
and different IITs. Succeeding in a DRDO interview requires thorough
preparation of four-six academic subjects and a deep understanding of the
organization's objectives and projects.&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;
  
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  &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: start; white-space: pre-wrap;"&gt;&lt;b&gt;&lt;span style="font-family: arial;"&gt;Tips for DRDO interviews&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Here are some valuable tips to help you prepare for DRDO
interviews and increase your chances of success:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;b&gt;Research DRDO: &lt;/b&gt;Gain a comprehensive understanding of DRDO's
mission, ongoing projects, and recent advancements. This knowledge will
demonstrate your genuine interest in the organization and help you align your
preparation accordingly.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;b&gt;Technical Knowledge:&lt;/b&gt;&lt;span style="font-weight: normal;"&gt; Brush up on your technical knowledge, focusing
on areas that align with DRDO's research domains. Be prepared to discuss your
academic background, projects you've worked on, and any practical experience
you have in those areas.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;b&gt;Problem-solving Skills: &lt;/b&gt;&lt;span style="font-weight: normal;"&gt;DRDO seeks candidates who can approach
complex problems with innovative solutions. Practice solving technical problems
and be ready to explain your problem-solving approach and methodology during
the interview.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="font-weight: normal;"&gt;
  
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  &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;b&gt;Stay Updated:&lt;/b&gt;&lt;span style="font-weight: normal;"&gt; Stay abreast of the latest developments and trends in
defense technology. Familiarize yourself with emerging technologies, defense
policies, and global security challenges. Being well-informed will help you
engage in meaningful discussions during the interview.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;b&gt;Communication Skills:&lt;/b&gt;&lt;span style="font-weight: normal;"&gt; Effective communication is crucial during
DRDO interviews. Practice articulating your thoughts clearly and concisely. Be
prepared to explain technical concepts in simple terms that can be understood
by non-experts.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;p class="MsoNormal" style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&lt;b&gt;Mock Interviews:&lt;/b&gt;&lt;span style="font-weight: normal;"&gt; Conduct mock interviews with friends, mentors, or
career counselors to simulate the interview experience. These practice sessions
will help refine your responses, improve your confidence, and identify areas
needing further development.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;

&lt;h4 style="--tw-border-spacing-x: 0; --tw-border-spacing-y: 0; --tw-ring-color: rgba(69,89,164,.5); --tw-ring-offset-color: #fff; --tw-ring-offset-shadow: 0 0 transparent; --tw-ring-offset-width: 0px; --tw-ring-shadow: 0 0 transparent; --tw-rotate: 0; --tw-scale-x: 1; --tw-scale-y: 1; --tw-scroll-snap-strictness: proximity; --tw-shadow-colored: 0 0 transparent; --tw-shadow: 0 0 transparent; --tw-skew-x: 0; --tw-skew-y: 0; --tw-translate-x: 0; --tw-translate-y: 0; box-sizing: border-box; text-align: left; white-space: pre-wrap;"&gt;&lt;span style="font-family: arial;"&gt;&lt;o:p&gt;&amp;nbsp;&lt;/o:p&gt;&lt;b style="text-align: center;"&gt;DRDO Interview Questions as Aerospace Structure Engineer&lt;/b&gt;&lt;/span&gt;&lt;/h4&gt;

&lt;p style="text-align: left;"&gt;&lt;span style="text-align: justify;"&gt;&lt;span style="font-family: arial;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;To give you an idea of the type of questions you may
encounter in a DRDO interview, here are some sample questions:&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;ol style="text-align: left;"&gt;&lt;ol&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;What is the cl vs alpha curve for sweep wings
and delta wings?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;What are the differences between sweeping
forward and backward wings explain as Structure engineer?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;Can we rope consider as a structure or not? If
yes then why and if not then why not?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;What is the use of FEM and where we used it?
Here we solved which kind of differential equations using FEM?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;How to define FEM formulation for any
differential equation?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;F=k*x^2 is vibration or not? Why?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;Write the SHM equation for a spring-mass system?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;The time period of the spring-mass system for
parallel and series systems?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;For a simply supported beam, we applied a load
on the mid-section to find out the deflection and other things by FEM?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;What is flutter?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;When divergence occurs?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;Give 3 different lamina orientations (0°, 90°, perpendicular
to length) laminate. Which laminate is more stable and why?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;Give 3 different lamina orientations (0°, 90°, perpendicular
to length) laminate. How to solve using FEM?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;In lamina, we first find out global stress/
local stress? And how to apply it to the system?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;In the stress-strain relation for lamina T is the?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;&lt;span style="text-align: justify; text-indent: -0.25in;"&gt;Young's modulus formula for lamina for each
direction?&lt;/span&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span style="font-family: arial;"&gt;What if the failure occurs in the lamina and how
will we be checked?&amp;nbsp;&lt;/span&gt;&lt;/li&gt;&lt;/ol&gt;&lt;/ol&gt;&lt;p&gt;&lt;/p&gt;&lt;h2 style="text-align: center;"&gt;

&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;
  
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  &lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Basically, they start from the basics and asked some conceptual questions based on the general scenario. Experts panels check our thinking process for solving problems.&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; I hope this article has provided you with a valuable understanding
of DRDO interviews and equipped you with interview questions to encourage your
preparation. Remember to research extensively, focus on enhancing your
technical knowledge, and practice problem-solving skills. With thorough
preparation and confidence, you can ace your DRDO interview and take a step
closer to a rewarding career in defense research and development. Best of luck
on your journey, and thank you for reading!&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: justify;"&gt;&lt;span style="font-weight: normal;"&gt;&lt;span style="font-family: arial; font-size: small;"&gt;
  
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  &lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;p class="MsoNormal" style="text-align: justify;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;&lt;/h2&gt;&lt;p&gt;&lt;/p&gt;</description><link>https://aerogatetopper.blogspot.com/2023/05/DRDO-interview-questions-for-Aerospace-Structure.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEibPtM_9eB891iH90RGRSO9Fq9sxmwsKR-9PTi95AIqBsPrDMAXoxSTUkIvry5l9XOYGB1Z8YglFHFyQ3tKAj8IhJFLKw7m9kTKAM3dTaCF9DUKoJTDGtI7SlJ06XMGTm6V6lYPJlKUug962r-fS2HJtVOOvUjqx9Yfd15qOl9YiwT_1wxeTjzMprvWmQ=s72-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-1898725917796233787</guid><pubDate>Thu, 26 Jan 2023 14:00:00 +0000</pubDate><atom:updated>2025-01-20T19:51:58.304+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">flight mechanics</category><category domain="http://www.blogger.com/atom/ns#">revision notes</category><title>Flight Mechanics revision notes for GATE Aerospace</title><description>&lt;p&gt;&lt;span style="font-size: medium;"&gt;In this post I will share f&lt;b&gt;light mechanics&lt;/b&gt; and &lt;b&gt;flight dynamics &lt;/b&gt;revision with specific points introduce that are very useful in upcoming &lt;b&gt;GATE Aerospace Engineering&amp;nbsp;&lt;/b&gt;exam. In this file I will cover entire &lt;b&gt;flight mechanics &lt;/b&gt;and &lt;b&gt;flight dynamics&lt;/b&gt; syllabus with some tips &amp;amp; tricks. I hope this file work as booster in your preparation.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://aerogatetopper.blogspot.com/" style="margin-left: 1em; margin-right: 1em;" target="_blank"&gt;&lt;img alt="Flight mechanics revision notes for GATE Aerospace" border="0" data-original-height="328" data-original-width="584" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQsJh_woM54iESg_NieRDrBC_XCbEW3Tr5D30MlHD3YgdVErgkU5XxLm1NnkW6f-TcShT2VgRn6xvKrz0jqU6TC-Uecakc4_u3iQtRgiLCPiL9zafYFewMj7EiHP9YDfBM0haXsf8w_DpwUHFjd35Hl8eLbA0NoKAz6XphJl0e1AYy9Q78uwSHIdes7g/w354-h199/Aero%20Gate%20Topper.jpg" title="Flight mechanics revision notes for GATE Aerospace" width="354" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;br /&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;b&gt;Aircraft Structure Practice Test:-&amp;nbsp;&lt;a href="https://aerogatetopper.blogspot.com/2021/07/structure-practice-mock-test.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/div&gt;&lt;p&gt;&lt;/p&gt;&lt;p style="text-align: center;"&gt;&lt;b&gt;Formula sheet for revision-&amp;nbsp; &lt;a href="https://aerogatetopper.blogspot.com/2023/01/gate-aerospace-formula-revision-sheet.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;&lt;p style="text-align: center;"&gt;&lt;b&gt;Aircraft Structure notes:- &lt;a href="https://aerogatetopper.blogspot.com/2021/11/notes-for-aircraft-structure-basic-to-advance.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;&lt;p style="text-align: center;"&gt;&lt;b&gt;Aircraft Propulsion notes:- &lt;a href="https://aerogatetopper.blogspot.com/2022/02/aircraft-propulsion-notes-part-1.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;

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&lt;p style="text-align: center;"&gt;&lt;b&gt;Gas dynamics Notes:-&amp;nbsp; &lt;a href="https://aerogatetopper.blogspot.com/2021/12/gas-dynamics-notes-for-gate-ae.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;&lt;p style="text-align: center;"&gt;&lt;b&gt;Propulsion Formula sheet:-&amp;nbsp; &lt;a href="https://aerogatetopper.blogspot.com/2022/02/aircraft-propulsion-formula-revision.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;&lt;p style="text-align: center;"&gt;&lt;b&gt;GATE previous year papers with answer key:- &lt;a href="https://aerogatetopper.blogspot.com/2021/05/gate-ae-previous-year-question-papers.html"&gt;Click here&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;&lt;p style="text-align: center;"&gt;&lt;br /&gt;&lt;/p&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;In this file we have cover all these topics concepts&amp;nbsp; related to some conceptual problems and revision purpose.&amp;nbsp;&lt;/span&gt;&lt;span face="Arial, &amp;quot;sans-serif&amp;quot;" style="font-size: medium;"&gt;We hope it'll helpful for you people and we have more notes to provide you regarding &lt;b&gt;GATE Aerospace Engineering.&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span face="Arial, &amp;quot;sans-serif&amp;quot;" style="font-size: medium;"&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;span face="Arial, &amp;quot;sans-serif&amp;quot;" style="font-size: medium;"&gt;&lt;b&gt;Note:- If you required any help then comment and message on telegram.&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;span style="font-size: medium;"&gt;&#128071;&#128071;&amp;nbsp;&lt;b&gt;Notes here&amp;nbsp;&lt;/b&gt;&#128071;&#128071;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;span style="color: red; font-size: medium;"&gt;&lt;b&gt;Download link given below&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: center;"&gt;&lt;span style="font-size: medium;"&gt;&lt;b&gt;&lt;script async="" crossorigin="anonymous" src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"&gt;&lt;/script&gt;
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  &lt;/b&gt;&lt;/span&gt;&lt;/div&gt;</description><link>https://aerogatetopper.blogspot.com/2023/01/flight-mechanics-revision-notes-for-GATE-AE.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQsJh_woM54iESg_NieRDrBC_XCbEW3Tr5D30MlHD3YgdVErgkU5XxLm1NnkW6f-TcShT2VgRn6xvKrz0jqU6TC-Uecakc4_u3iQtRgiLCPiL9zafYFewMj7EiHP9YDfBM0haXsf8w_DpwUHFjd35Hl8eLbA0NoKAz6XphJl0e1AYy9Q78uwSHIdes7g/s72-w354-h199-c/Aero%20Gate%20Topper.jpg" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-6454117883440708110</guid><pubDate>Wed, 04 Jan 2023 07:51:00 +0000</pubDate><atom:updated>2023-05-29T19:23:14.868+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">INTERVIEW</category><category domain="http://www.blogger.com/atom/ns#">Strength of Material</category><title>Strength of Material Interview Related Questions Part-1</title><description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;&lt;p style="text-align: left;"&gt;&lt;span style="font-size: large;"&gt;In this post I have answered some important Strength of material interview related questions. I think that it is useful for your preparation and boost your knowledge. These questions are also helpful for your exam preparations and also your interview preparation like&amp;nbsp;&lt;b&gt;ISRO, DRDO, Research Interviews and all PSU's&lt;/b&gt;.&lt;/span&gt;&lt;/p&gt;

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&lt;p style="text-align: left;"&gt;&lt;a href="https://aerogatetopper.blogspot.com/" rel="nofollow" style="margin-left: 1em; margin-right: 1em; text-align: center;" target="_blank"&gt;&lt;img alt="Basic aerodynamics questions" border="0" data-original-height="217" data-original-width="454" height="191" src="https://blogger.googleusercontent.com/img/a/AVvXsEibPtM_9eB891iH90RGRSO9Fq9sxmwsKR-9PTi95AIqBsPrDMAXoxSTUkIvry5l9XOYGB1Z8YglFHFyQ3tKAj8IhJFLKw7m9kTKAM3dTaCF9DUKoJTDGtI7SlJ06XMGTm6V6lYPJlKUug962r-fS2HJtVOOvUjqx9Yfd15qOl9YiwT_1wxeTjzMprvWmQ=w400-h191" title="Basic aerodynamics questions" width="400" /&gt;&lt;/a&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.1 What you meant by strength &amp;amp; material in Strength of material?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;In Strength of Material here &lt;b&gt;strength&lt;/b&gt; means the property of the material. And &lt;b&gt;material &lt;/b&gt;means the engineering material generally we study here on solid material.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.2 What is the difference between Solid and Fluid?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;Main difference between due to applied load-&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Solid:-&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;1. If we applied force on solid the solid molecular bond resist the force that's why here stress induced.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;2. Basically in Strength of material strength term related to stress due to internal resistant in solid.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;3. In solid stress induced due to force.&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: left;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc71XtB4lGWMFtV0F0wiRRUdm45mJ-oOhX7N8ZMH-IKeb3QJgueujw6pix9R_RvlGgv4BPPqAY-qh2FBBh9zjzXoXjlbWxgNbwhs2R4v3rQtXtFYWs9RKNnvyYtPiSXD_B1mU5iU5oyD4CCOS0qidCsF2gcbubaf3Jg6MsgeEPzz-N0H9pmTCvqsbr9Q/s540/when%20resist%20the%20force.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"&gt;&lt;span style="font-size: medium;"&gt;&lt;img border="0" data-original-height="377" data-original-width="540" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc71XtB4lGWMFtV0F0wiRRUdm45mJ-oOhX7N8ZMH-IKeb3QJgueujw6pix9R_RvlGgv4BPPqAY-qh2FBBh9zjzXoXjlbWxgNbwhs2R4v3rQtXtFYWs9RKNnvyYtPiSXD_B1mU5iU5oyD4CCOS0qidCsF2gcbubaf3Jg6MsgeEPzz-N0H9pmTCvqsbr9Q/s320/when%20resist%20the%20force.png" width="320" /&gt;&lt;/span&gt;&lt;/a&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Fluid:-&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;1. If we&amp;nbsp;applied force on fluid/liquid the molecular of fluid is free (fluid don't resist the force)&amp;nbsp; that's why here not stress induced.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;2. Stress in fluid due to molecular attraction that's known as viscosity.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;3. In fluid Force induced due to shear stress.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.3 What is the difference between Stress and Pressure?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td style="text-align: center;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Stress&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;td style="text-align: center;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Pressure&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;1. stress is ratio of internal resistance force to area.&lt;/span&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;1. Pressure is the intermolecular collision in fluid.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;2.&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc71XtB4lGWMFtV0F0wiRRUdm45mJ-oOhX7N8ZMH-IKeb3QJgueujw6pix9R_RvlGgv4BPPqAY-qh2FBBh9zjzXoXjlbWxgNbwhs2R4v3rQtXtFYWs9RKNnvyYtPiSXD_B1mU5iU5oyD4CCOS0qidCsF2gcbubaf3Jg6MsgeEPzz-N0H9pmTCvqsbr9Q/s540/when%20resist%20the%20force.png" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;span style="font-size: medium;"&gt;&lt;img border="0" data-original-height="377" data-original-width="540" height="223" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc71XtB4lGWMFtV0F0wiRRUdm45mJ-oOhX7N8ZMH-IKeb3QJgueujw6pix9R_RvlGgv4BPPqAY-qh2FBBh9zjzXoXjlbWxgNbwhs2R4v3rQtXtFYWs9RKNnvyYtPiSXD_B1mU5iU5oyD4CCOS0qidCsF2gcbubaf3Jg6MsgeEPzz-N0H9pmTCvqsbr9Q/s320/when%20resist%20the%20force.png" width="320" /&gt;&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;2.&amp;nbsp;&lt;/span&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIe04M-fQYpNw4FMMlEdPVo_qMhR36mDU4Hxt0j_43FddZlrGF7QWAucHXLX2V4pxzthAhdvPWctClwvdUkzHwrJpyvGDbOQtzC09pqe_qjVUdKKL6nK8fvS1ae07XJPUZr4AeylB8bKOP2EsRDMNt4Wli-bkLPYpvL8klhWYgO11GH6wbFD9jwDNxLQ/s357/Pressure.png" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;span style="font-size: medium;"&gt;&lt;img border="0" data-original-height="241" data-original-width="357" height="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIe04M-fQYpNw4FMMlEdPVo_qMhR36mDU4Hxt0j_43FddZlrGF7QWAucHXLX2V4pxzthAhdvPWctClwvdUkzHwrJpyvGDbOQtzC09pqe_qjVUdKKL6nK8fvS1ae07XJPUZr4AeylB8bKOP2EsRDMNt4Wli-bkLPYpvL8klhWYgO11GH6wbFD9jwDNxLQ/s320/Pressure.png" width="320" /&gt;&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;3. Stress is tensile, compressive and shear nature.&lt;/span&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;3. It is always Normal &amp;amp; Compressive nature.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;4. Stress is depends on Force.&lt;/span&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;4. Pressure doesn't depends on force. But force is depends on pressure.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;5. Stress is output due to applied resistance force.&lt;/span&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;5. Pressure force is output due to applied pressure.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;6. stress is output.&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/td&gt;&lt;td&gt;&lt;span style="font-size: medium;"&gt;6. Pressure is input.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.4 What is the difference between Stress and Strength?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;table border="1" cellpadding="1" cellspacing="1" style="text-align: center; width: 500px;"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Stress&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;td&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Strength&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;1. It is variable term.&lt;/span&gt;&lt;/td&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;1. It is constant for material (material property)&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;2. It depends on resistance load.&lt;/span&gt;&lt;/td&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;3. It doesn't depends on applied load.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;3. Unit- N/m^2&lt;/span&gt;&lt;/td&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;4. Unit- N/m^2&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;5. Stress is ratio of resistance force to area of cross-section.&lt;/span&gt;&lt;/td&gt;&lt;td style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;5. Maximum stress induced upto failure point.&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;p&gt;
  
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  &lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.5 Why we study mild steel stress-strain diagram?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;Because of that is very informative diagram. In this graph we study many type of strength -&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4GsrBoet-5soSOgRgzbhO1LN8pAUyMugEAJwPuVTcNztwTiDqeBEQJWFvjHKz42bJn60wrXT2vYrgQoTHgW9GmzR3RGsGX4F80hAVkLoZkCIUQinzreCdekuo9Y3yIbHDJv2oczjdtBJrvlo3HkPftdYsWhNOAEEblUBgPodpmih3fVvopCaZDgGEfQ/s3978/IMG20230104125332.jpg" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;img border="0" data-original-height="2417" data-original-width="3978" height="389" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4GsrBoet-5soSOgRgzbhO1LN8pAUyMugEAJwPuVTcNztwTiDqeBEQJWFvjHKz42bJn60wrXT2vYrgQoTHgW9GmzR3RGsGX4F80hAVkLoZkCIUQinzreCdekuo9Y3yIbHDJv2oczjdtBJrvlo3HkPftdYsWhNOAEEblUBgPodpmih3fVvopCaZDgGEfQ/w640-h389/IMG20230104125332.jpg" width="640" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;br /&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;p&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;1. Yield strength&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;2. Ultimate strength&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;3. Fracture/ Failure strength&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.6 What do you mean by failure in engineering term?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;span style="font-size: medium;"&gt;Failures for engineering means far before fracture point. For engineering failure means yield point/ permanent deformation/ plastic deformation.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.7 If we applied force on a body will the stress induce in that or not?&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;May or may not be, When I applied a force if body resist the force then in the body stress will be induced.&lt;/span&gt;&lt;/div&gt;&lt;div style="text-align: left;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc71XtB4lGWMFtV0F0wiRRUdm45mJ-oOhX7N8ZMH-IKeb3QJgueujw6pix9R_RvlGgv4BPPqAY-qh2FBBh9zjzXoXjlbWxgNbwhs2R4v3rQtXtFYWs9RKNnvyYtPiSXD_B1mU5iU5oyD4CCOS0qidCsF2gcbubaf3Jg6MsgeEPzz-N0H9pmTCvqsbr9Q/s540/when%20resist%20the%20force.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"&gt;&lt;span style="font-size: medium;"&gt;&lt;img border="0" data-original-height="377" data-original-width="540" height="272" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc71XtB4lGWMFtV0F0wiRRUdm45mJ-oOhX7N8ZMH-IKeb3QJgueujw6pix9R_RvlGgv4BPPqAY-qh2FBBh9zjzXoXjlbWxgNbwhs2R4v3rQtXtFYWs9RKNnvyYtPiSXD_B1mU5iU5oyD4CCOS0qidCsF2gcbubaf3Jg6MsgeEPzz-N0H9pmTCvqsbr9Q/w392-h272/when%20resist%20the%20force.png" width="392" /&gt;&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&lt;!--[if gte vml 1]&gt;&lt;v:group id="_x0000_s1037" style='position:absolute;
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&lt;/tbody&gt;&lt;/table&gt;&lt;/div&gt;&lt;div style="text-align: left;"&gt;&lt;span style="font-size: medium;"&gt;But I applied a force if body freely move then in the body stress will be not induced.&amp;nbsp;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;&lt;br /&gt;&lt;/p&gt;&lt;div style="text-align: left;"&gt;&lt;span style="font-size: large;"&gt;&amp;nbsp;&lt;/span&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA8J1c2Wjd1wLZPIah-66vpygZ08IGfaJ3lg7sD4HGoUqG0ZtQ35V8lgrIfJvnVq3dFLV5y1vhl3WTHlks-XWTz07wMzawvi_ESdVVSDNFs14SlnahaeOIRIrkf07O2wqw5hD35rhdKwDVFzCbLfYjVhGrRWUDkwnYbEccH4u1Z1_G3k3n6c91grV_Gg/s549/when%20we%20applied%20load%20body%20will%20be%20move.png" style="font-size: large; margin-left: 1em; margin-right: 1em; text-align: center;"&gt;&lt;img border="0" data-original-height="260" data-original-width="549" height="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiA8J1c2Wjd1wLZPIah-66vpygZ08IGfaJ3lg7sD4HGoUqG0ZtQ35V8lgrIfJvnVq3dFLV5y1vhl3WTHlks-XWTz07wMzawvi_ESdVVSDNFs14SlnahaeOIRIrkf07O2wqw5hD35rhdKwDVFzCbLfYjVhGrRWUDkwnYbEccH4u1Z1_G3k3n6c91grV_Gg/w455-h216/when%20we%20applied%20load%20body%20will%20be%20move.png" width="455" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;div style="text-align: left;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div style="text-align: left;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div style="text-align: left;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Q.8 What means by Elastic limit &amp;amp; Plastic limit?&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;&lt;b&gt;Elastic limit:-&lt;/b&gt; It is that point upto which if we load the body, body will deform but when we remove the load body will comes in original position (shape &amp;amp; size) without any permanent deformation or residual strain.&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4GsrBoet-5soSOgRgzbhO1LN8pAUyMugEAJwPuVTcNztwTiDqeBEQJWFvjHKz42bJn60wrXT2vYrgQoTHgW9GmzR3RGsGX4F80hAVkLoZkCIUQinzreCdekuo9Y3yIbHDJv2oczjdtBJrvlo3HkPftdYsWhNOAEEblUBgPodpmih3fVvopCaZDgGEfQ/s3978/IMG20230104125332.jpg" style="margin-left: 1em; margin-right: 1em; text-align: center;"&gt;&lt;img border="0" data-original-height="2417" data-original-width="3978" height="389" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4GsrBoet-5soSOgRgzbhO1LN8pAUyMugEAJwPuVTcNztwTiDqeBEQJWFvjHKz42bJn60wrXT2vYrgQoTHgW9GmzR3RGsGX4F80hAVkLoZkCIUQinzreCdekuo9Y3yIbHDJv2oczjdtBJrvlo3HkPftdYsWhNOAEEblUBgPodpmih3fVvopCaZDgGEfQ/w640-h389/IMG20230104125332.jpg" width="640" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: medium;"&gt;&lt;b&gt;Plastic limit:-&lt;/b&gt;&amp;nbsp; It is that point which if we load the body, body will deform but when we remove the load body will comes in original position (shape &amp;amp; size) with some kind of deformation or permanent deformation. That permanent deformation point called &lt;b&gt;Yield Point&lt;/b&gt;.&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: large;"&gt;If you like this &#128070;&#128070;&#128070; content and it is helpful for you and required for more parts like that then &lt;b&gt;comment below &lt;/b&gt;&#128071;&#128071;&#128071;.&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;
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</description><link>https://aerogatetopper.blogspot.com/2023/01/httpsaerogatetopper.blogspot.com202301strength-of-material-interview-related-quetions-part-1.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEibPtM_9eB891iH90RGRSO9Fq9sxmwsKR-9PTi95AIqBsPrDMAXoxSTUkIvry5l9XOYGB1Z8YglFHFyQ3tKAj8IhJFLKw7m9kTKAM3dTaCF9DUKoJTDGtI7SlJ06XMGTm6V6lYPJlKUug962r-fS2HJtVOOvUjqx9Yfd15qOl9YiwT_1wxeTjzMprvWmQ=s72-w400-h191-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-7021945920121681507</guid><pubDate>Sun, 18 Dec 2022 12:26:00 +0000</pubDate><atom:updated>2022-12-18T18:10:14.272+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">aerodynamics</category><category domain="http://www.blogger.com/atom/ns#">aerodynamics mock test</category><category domain="http://www.blogger.com/atom/ns#">Fluid Mechanics</category><title>Basic Aerodynamics questions</title><description>&lt;p&gt;&amp;nbsp;&lt;/p&gt;&lt;h2 style="text-align: center;"&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111; font-size: large;"&gt;&lt;b&gt;Basic Aerodynamics Question &amp;amp; Answer&lt;/b&gt;&lt;/span&gt;&lt;/h2&gt;&lt;div&gt;&lt;span style="font-size: large;"&gt;&lt;span style="color: #111111;"&gt;&lt;span style="background-color: white;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: large;"&gt;&lt;span style="color: #111111;"&gt;&lt;span style="background-color: white;"&gt;Here we added &lt;b&gt;basic aerodynamics and fluid mechanics questions&lt;/b&gt;. Here question type are &lt;b&gt;MCQ's MSQ's &amp;amp; NAT's questions&lt;/b&gt; ask in many different exam like &lt;b&gt;GATE, HAL, ISRO &lt;/b&gt;&amp;amp; Technical exams etc. We have collect some types of pattern based question collect for practice.&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: white; color: #111111;"&gt;Here we will be learn about basic aerodynamics and fluid mechanics questions.&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: large;"&gt;&lt;span style="background-color: white; color: #111111;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;h4 style="text-align: left;"&gt;&lt;span style="font-size: large;"&gt;&lt;span style="color: #111111;"&gt;&lt;b style="background-color: #3d85c6; color: black;"&gt;We hope these problems are helpful for you. For more questions stay with us.&lt;/b&gt;&lt;/span&gt;&lt;/span&gt;&lt;/h4&gt;
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&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://aerogatetopper.blogspot.com/" rel="nofollow" style="font-size: medium; margin-left: 1em; margin-right: 1em; text-align: center;" target="_blank"&gt;&lt;img alt="Basic aerodynamics questions" border="0" data-original-height="217" data-original-width="454" height="191" src="https://blogger.googleusercontent.com/img/a/AVvXsEibPtM_9eB891iH90RGRSO9Fq9sxmwsKR-9PTi95AIqBsPrDMAXoxSTUkIvry5l9XOYGB1Z8YglFHFyQ3tKAj8IhJFLKw7m9kTKAM3dTaCF9DUKoJTDGtI7SlJ06XMGTm6V6lYPJlKUug962r-fS2HJtVOOvUjqx9Yfd15qOl9YiwT_1wxeTjzMprvWmQ=w400-h191" title="Basic aerodynamics questions" width="400" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div style="text-align: left;"&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111; font-size: large;"&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111; font-size: large;"&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class="question" style="text-align: justify;"&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111;"&gt;&lt;b&gt;1.&amp;nbsp;&lt;/b&gt;&lt;/span&gt;&lt;b&gt;&lt;span style="text-indent: -0.05pt;"&gt;The figure shows the developing zone and the fully developed region in a pipe&lt;/span&gt;&lt;span style="letter-spacing: 0.05pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;flow&lt;/span&gt;&lt;span style="letter-spacing: -0.5pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;where&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;the&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;steady&lt;/span&gt;&lt;span style="letter-spacing: -0.5pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;flow&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;takes&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;place&lt;/span&gt;&lt;span style="letter-spacing: -0.5pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;from&lt;/span&gt;&lt;span style="letter-spacing: -0.7pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;left&lt;/span&gt;&lt;span style="letter-spacing: -0.5pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;to&lt;/span&gt;&lt;span style="letter-spacing: -0.5pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;right.&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;The&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;wall&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;shear&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;stress&lt;/span&gt;&lt;span style="letter-spacing: -0.45pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;in&lt;/span&gt;&lt;span style="letter-spacing: 0.05pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;the&lt;/span&gt;&lt;span style="letter-spacing: 0.6pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;sections&lt;/span&gt;&lt;span style="letter-spacing: 0.7pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;A,&lt;/span&gt;&lt;span style="letter-spacing: 0.65pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;B,&lt;/span&gt;&lt;span style="letter-spacing: 0.65pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;C,&lt;/span&gt;&lt;span style="letter-spacing: 0.65pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;and&lt;/span&gt;&lt;span style="letter-spacing: 0.75pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;D&lt;/span&gt;&lt;span style="letter-spacing: 0.65pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;are&lt;/span&gt;&lt;span style="letter-spacing: 0.65pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;given&lt;/span&gt;&lt;span style="letter-spacing: 0.7pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;by&lt;/span&gt;&lt;span style="letter-spacing: 0.8pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: Cambria, &amp;quot;serif&amp;quot;; text-indent: -0.05pt;"&gt;&#120591;&lt;sub&gt;Æ&lt;/sub&gt;,&lt;span style="letter-spacing: -0.2pt;"&gt;&amp;nbsp;&lt;/span&gt;&#120591;&lt;sub&gt;B&lt;/sub&gt;,&lt;span style="letter-spacing: -0.1pt;"&gt;&amp;nbsp;&lt;/span&gt;&#120591;&lt;sub&gt;C&lt;/sub&gt;,&lt;span style="letter-spacing: 1.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;and&lt;/span&gt;&lt;span style="letter-spacing: 0.7pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: Cambria, &amp;quot;serif&amp;quot;; text-indent: -0.05pt;"&gt;&#120591;&lt;sub&gt;D&lt;/sub&gt;,&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;respectively.&lt;/span&gt;&lt;span style="letter-spacing: 0.55pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;Select&lt;/span&gt;&lt;span style="letter-spacing: 0.65pt; text-indent: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="text-indent: -0.05pt;"&gt;the&amp;nbsp;&lt;/span&gt;correct&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;statement.&amp;nbsp;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp; &lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;[&lt;span style="color: red;"&gt;MCQ&lt;/span&gt;]&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class="question"&gt;&lt;div class="separator" style="clear: both; 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font-size: 11pt;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class="question"&gt;&lt;table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 0.25pt; mso-border-alt: solid black .5pt; mso-border-insideh: .5pt solid black; mso-border-insidev: .5pt solid black; mso-padding-alt: 0in 0in 0in 0in; mso-table-layout-alt: fixed; mso-yfti-tbllook: 480;"&gt;&lt;tbody&gt;&lt;tr style="height: 25.95pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;"&gt;&lt;td style="border: 1pt solid black; height: 25.95pt; mso-border-alt: solid black .5pt; padding: 0in; width: 149.55pt;" valign="top" width="199"&gt;&lt;p class="TableParagraph" style="margin-bottom: 0in; margin-left: 22.0pt; margin-right: 0in; margin-top: .2pt; margin: 0.2pt 0in 0in 22pt;"&gt;&lt;b&gt;1.&lt;span style="letter-spacing: 1.4pt;"&gt;&amp;nbsp;&lt;/span&gt;Reynolds&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;number&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style="border-left: none; border: 1pt solid black; height: 25.95pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in; width: 165.1pt;" valign="top" width="220"&gt;&lt;p class="TableParagraph" style="margin-bottom: 0in; margin-left: 21.95pt; margin-right: 0in; margin-top: .2pt; margin: 0.2pt 0in 0in 21.95pt; tab-stops: 55.8pt;"&gt;&lt;b&gt;i.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Wave&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;drag&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 25.9pt; mso-yfti-irow: 1;"&gt;&lt;td style="border-top: none; border: 1pt solid black; height: 25.9pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in; width: 149.55pt;" valign="top" width="199"&gt;&lt;p class="TableParagraph" style="margin-bottom: 0in; margin-left: 22.0pt; margin-right: 0in; margin-top: .1pt; margin: 0.1pt 0in 0in 22pt;"&gt;&lt;b&gt;2.&lt;span style="letter-spacing: 1.45pt;"&gt;&amp;nbsp;&lt;/span&gt;Froude&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;number&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style="border-bottom: 1pt solid black; 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margin-top: .15pt; margin: 0.15pt 0in 0in 22pt;"&gt;&lt;b&gt;3.&lt;span style="letter-spacing: 1.75pt;"&gt;&amp;nbsp;&lt;/span&gt;Mach&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;number&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style="border-bottom: 1pt solid black; border-left: none; border-right: 1pt solid black; border-top: none; height: 25.85pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in; width: 165.1pt;" valign="top" width="220"&gt;&lt;p class="TableParagraph" style="margin-bottom: 0in; margin-left: 21.95pt; margin-right: 0in; margin-top: .15pt; margin: 0.15pt 0in 0in 21.95pt; tab-stops: 55.8pt;"&gt;&lt;b&gt;iii.&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;span style="letter-spacing: -0.05pt;"&gt;Viscous&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;drag&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style="height: 25.95pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;"&gt;&lt;td style="border-top: none; border: 1pt solid black; height: 25.95pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in; width: 149.55pt;" valign="top" width="199"&gt;&lt;p class="TableParagraph" style="margin-bottom: 0in; margin-left: 22.0pt; margin-right: 0in; margin-top: .15pt; margin: 0.15pt 0in 0in 22pt;"&gt;&lt;b&gt;4.&lt;span style="letter-spacing: 1.7pt;"&gt;&amp;nbsp;&lt;/span&gt;Weber&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;number&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style="border-bottom: 1pt solid black; border-left: none; border-right: 1pt solid black; border-top: none; height: 25.95pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in; width: 165.1pt;" valign="top" width="220"&gt;&lt;p class="TableParagraph" style="margin-bottom: 0in; margin-left: 22.0pt; margin-right: 0in; 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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question"&gt;&lt;b&gt;4.&amp;nbsp;&lt;/b&gt;&lt;b&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;Which&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;of&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;the&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;following&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;statement(s)&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;regarding&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;a&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.8pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;venturimeter&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;is/are&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 0.8pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;correct?&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp; [&lt;span style="color: red;"&gt;MSQ&lt;/span&gt;]&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;ul class="answers"&gt;&lt;b&gt;&lt;input id="question4a" name="question4" type="radio" value="a" /&gt;&amp;nbsp;A)&amp;nbsp;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;In&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;direction&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;flow,&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;it&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;consists&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;converging&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;section,&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;throat,&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;and&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: -2.7pt;"&gt;&amp;nbsp;&lt;/span&gt;diverging&lt;span style="letter-spacing: -0.1pt;"&gt;&amp;nbsp;&lt;/span&gt;section.&lt;/span&gt;&lt;br /&gt;&lt;input id="question4b" name="question4" type="radio" value="b" /&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; 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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question"&gt;&lt;b&gt;5.&lt;/b&gt;&lt;b&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;Which&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;of&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;the&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;following&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;statement(s)&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: 1.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;is/are&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;true&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;for&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;streamlines&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;in&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;steady&lt;span style="letter-spacing: -2.75pt;"&gt;&amp;nbsp;&lt;/span&gt;incompressible&lt;span style="letter-spacing: -0.2pt;"&gt;&amp;nbsp;&lt;/span&gt;flow?&amp;nbsp; &amp;nbsp;[&lt;span style="color: red;"&gt;MSQ&lt;/span&gt;]&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;ul class="answers"&gt;&lt;b&gt;&lt;input id="question5a" name="question5" type="radio" value="a" /&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US;"&gt;A) Two&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;streamlines&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;cannot&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;intersect&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;each&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;other.&lt;/span&gt;&lt;br /&gt;&lt;input id="question5b" name="question5" type="radio" value="b" /&gt;&amp;nbsp;B)&amp;nbsp;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US;"&gt;Flow&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;rate&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;increases&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;between&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;two&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;diverging&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;streamlines.&lt;/span&gt;&lt;br /&gt;&lt;input id="question5c" name="question5" type="radio" value="c" /&gt;&amp;nbsp;C)&amp;nbsp;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US;"&gt;Flow&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;rate&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;decreases&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;between&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;two&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;diverging&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;streamlines.&lt;/span&gt;&lt;br /&gt;&lt;input id="question5d" name="question5" type="radio" value="d" /&gt;&amp;nbsp;D)&amp;nbsp;&lt;label&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; 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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question" style="text-align: justify;"&gt;&lt;b&gt;6.&amp;nbsp;&lt;/b&gt;&lt;b&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;A&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;flow&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;has&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;velocity&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;potential&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;given&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;by&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Cambria, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;&#120601;&lt;span style="letter-spacing: -0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;=&lt;span style="letter-spacing: 1.3pt;"&gt;&amp;nbsp;&lt;/span&gt;&#119860;&#119909;&lt;sup&gt;3&lt;/sup&gt;&lt;span style="letter-spacing: 1.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;where&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;‘&lt;i&gt;A&lt;/i&gt;’&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;non-zero&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt; mso-font-width: 105%;"&gt;constant.&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt; mso-font-width: 105%;"&gt;Which&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt; mso-font-width: 105%;"&gt;of&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;following&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;statement(s)&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;is/are&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;true&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;about&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;flow?&amp;nbsp; &amp;nbsp; [&lt;span style="color: red;"&gt;MSQ&lt;/span&gt;]&lt;span&gt;&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;ul class="answers"&gt;&lt;b&gt;&lt;input id="question6a" name="question6" type="radio" value="a" /&gt;&amp;nbsp;A)&amp;nbsp;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;The&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.65pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;flow&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.5pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;is&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.55pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;incompressible.&lt;/span&gt;&lt;br /&gt;&lt;input id="question6b" name="question6" type="radio" value="b" /&gt;&amp;nbsp;B)&amp;nbsp;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;The&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.7pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;flow&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.55pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;is&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.6pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;irrotational.&lt;/span&gt;&lt;br /&gt;&lt;input id="question6c" name="question6" type="radio" value="c" /&gt;&amp;nbsp;C)&amp;nbsp;&lt;label&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;The&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.65pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;flow&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.5pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;has&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.55pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;local&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.5pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; 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mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;acceleration.&lt;/span&gt;&lt;/label&gt;&lt;/b&gt;&lt;/ul&gt;&lt;style&gt;
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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question" style="text-align: justify;"&gt;&lt;b&gt;7.&amp;nbsp;&lt;/b&gt;&lt;b&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;A&lt;/span&gt;&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;boundary&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;layer&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;develops&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;due&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;to&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;a&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;two- dimensional&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;steady&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;flow&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;over&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;horizontal&lt;span style="letter-spacing: -2.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;flat&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;plate.&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;Consider&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;a&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;vertical&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;line&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;away&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;from&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;leading&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;edge&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;which&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;extends&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;from&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;the wall to the edge of the boundary layer. Which of the following&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;quantity/quantities is/are not constant along the vertical line?&amp;nbsp;&lt;span style="font-family: Cambria, &amp;quot;serif&amp;quot;;"&gt;&#119906; and &#119907;&amp;nbsp;&lt;/span&gt;represent&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;the components of velocity in the direction along the plate and normal to it,&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;respectively&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;and&lt;span style="letter-spacing: -0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;x&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;is&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;taken&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;along&lt;span style="letter-spacing: -0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;length&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;plate&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;while&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;p&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;is&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;pressure. (&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;Neglect&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;body&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt;"&gt;forces.)&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp; [&lt;span style="color: red;"&gt;MSQ&lt;/span&gt;]&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;ul class="answers"&gt;&lt;b&gt;&lt;input id="question7a" name="question7" type="radio" value="a" /&gt;&amp;nbsp;A)&amp;nbsp;&lt;span style="font-family: &amp;quot;Cambria&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-fareast-font-family: Cambria; mso-fareast-language: EN-US; mso-font-width: 105%; mso-hansi-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;&#119906;&lt;/span&gt;&lt;br /&gt;&lt;input id="question7b" name="question7" type="radio" value="b" /&gt;&amp;nbsp;B)&amp;nbsp;&lt;span style="font-family: &amp;quot;Cambria&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-fareast-font-family: Cambria; mso-fareast-language: EN-US; mso-font-width: 105%; mso-hansi-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;&#120597;&#119906;/&lt;/span&gt;&lt;span style="font-family: &amp;quot;Cambria&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-fareast-font-family: Cambria; mso-fareast-language: EN-US; mso-font-width: 105%; mso-hansi-font-family: &amp;quot;Times New Roman&amp;quot;;"&gt;&#120597;&#119909;&lt;/span&gt;&lt;br /&gt;&lt;input id="question7c" name="question7" type="radio" value="c" /&gt;&amp;nbsp;C)&amp;nbsp;&lt;span style="font-family: &amp;quot;Cambria&amp;quot;,&amp;quot;serif&amp;quot;; 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mso-font-width: 105%; mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;c'&lt;span style="letter-spacing: -0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;=&lt;span style="letter-spacing: -0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;span style="font-family: &amp;quot;Cambria&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;√&lt;span style="mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;2&lt;/span&gt;&lt;/span&gt;&lt;i&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%; mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;c&lt;/span&gt;&lt;/i&gt;&lt;br /&gt;&lt;input id="question8c" name="question8" type="radio" value="c" /&gt;&amp;nbsp;C)&amp;nbsp;&lt;label&gt;&lt;i&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; 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font-size: 12pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;f&lt;/span&gt;&lt;span style="font-size: 12pt; letter-spacing: 0.9pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: Symbol; font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;=&lt;/span&gt;&lt;span style="font-size: 11.5pt; letter-spacing: -1.05pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;Ux&lt;span style="letter-spacing: -0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;span style="font-family: Symbol; font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;+&lt;/span&gt;&lt;span style="font-size: 11.5pt; letter-spacing: 2.85pt; mso-bidi-font-size: 11.0pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11.5pt;"&gt;m/4&lt;/span&gt;&lt;span style="font-family: Symbol; font-size: 12pt;"&gt;p&lt;/span&gt;&lt;i&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%; mso-text-raise: 7.5pt; position: relative; top: -7.5pt;"&gt;&lt;span style="letter-spacing: 2.15pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;span style="font-size: 11.5pt;"&gt;ln(&lt;/span&gt;&lt;i&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;x&lt;/span&gt;&lt;/i&gt;&lt;sup&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;2&lt;/span&gt;&lt;/sup&gt;&lt;span style="font-size: 11.5pt; letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: Symbol; font-size: 11.5pt;"&gt;+&lt;/span&gt;&lt;span style="font-size: 11.5pt; letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;y&lt;span style="letter-spacing: -1.7pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;sup&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt; mso-font-width: 95%;"&gt;2&lt;/span&gt;&lt;/sup&gt;) The&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;stagnation&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;streamline&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;shown&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;in&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;figure.&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;Find&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;distance&lt;span style="letter-spacing: -0.95pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt;"&gt;aa&lt;/span&gt;&lt;/i&gt;&lt;span style="font-family: Symbol; font-size: 11.5pt; position: relative; top: -0.5pt;"&gt;¢&lt;/span&gt;&lt;span style="font-size: 11.5pt; letter-spacing: -1.35pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;.&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp;[&lt;span style="color: red;"&gt;MCQ&lt;/span&gt;]&lt;/span&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;&lt;div class="question"&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ2ebwn9JCQay8SdzpG-RlkAZoCz9hcu9zPzoPOi7LdqG_NN_HddYHP3U0YN7jFRq2Ew10HtJcSLXtpvHQTrH-hERuFBqaZnAYEcHd2uMH_NVvqmMoguqsvJ1q20Hl__mL7Xw6lDePmJdE5QDSYVMFEKkwuwgaOed-i9A5piHRGN8IoK2HbmOo6Q_GeQ/s446/Screenshot%202022-11-27%20165902.png" style="margin-left: 1em; 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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question" style="text-align: justify;"&gt;&lt;b&gt;10.&amp;nbsp;&lt;/b&gt;&lt;b&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;;"&gt;&lt;span style="font-size: 11pt;"&gt;A typical boundary layer over a flat plate has a linear velocity profile with zero&amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;velocity&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.5pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;at&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.6pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;the&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.6pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;wall&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.55pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;and&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.55pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;freestream&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.65pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;velocity,&lt;/span&gt;&lt;span style="font-size: 11pt; letter-spacing: -0.65pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;&lt;span style="letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;&lt;span style="font-size: medium;"&gt;U&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; letter-spacing: -0.05pt;"&gt;&lt;span style="font-size: medium;"&gt;∞&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;,&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.65pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;at&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.55pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.05pt; position: relative; top: -0.5pt;"&gt;the&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; letter-spacing: -0.65pt; position: relative; top: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt; position: relative; top: -0.5pt;"&gt;outer&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;edge&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;boundary&lt;span style="letter-spacing: -2.75pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;, &amp;quot;serif&amp;quot;; font-size: 11pt;"&gt;layer. 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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question"&gt;&lt;b&gt;11.&amp;nbsp;&lt;/b&gt;&lt;b&gt;&amp;nbsp;Identify&lt;span style="letter-spacing: 0.9pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;configuration(s)&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;in&lt;span style="letter-spacing: 0.8pt;"&gt;&amp;nbsp;&lt;/span&gt;which&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;steady&lt;span style="letter-spacing: 0.9pt;"&gt;&amp;nbsp;&lt;/span&gt;two-dimensional&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;internal&lt;span style="letter-spacing: 0.8pt;"&gt;&amp;nbsp;&lt;/span&gt;flow&lt;span style="letter-spacing: 0.9pt;"&gt;&amp;nbsp;&lt;/span&gt;may show&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;boundary&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;layer&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;separation&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;if&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;flow&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;direction&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;left&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;to&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;right.&lt;span&gt;&amp;nbsp;&amp;nbsp; 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text-align: center;"&gt;&lt;b&gt;C)&lt;/b&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAoC1JajyEPzDyJaWPLdghXBgZYNoktGcv-99--CcE_tCcmNC2ogd3DgOAFxSwtxCKGUXhgncD6qAu0I539efmxnLJ4jl-SGnf3-eE8HNkdwlYeUPS_PoNGILIq76akuax9QushFNSjMkhFNPfK8zwIcOtpfWIwaacFMRtTTeP6QPb7gzLHqkDdWSa2w/s252/Screenshot%202022-11-27%20170705.png" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;img border="0" data-original-height="154" data-original-width="252" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAoC1JajyEPzDyJaWPLdghXBgZYNoktGcv-99--CcE_tCcmNC2ogd3DgOAFxSwtxCKGUXhgncD6qAu0I539efmxnLJ4jl-SGnf3-eE8HNkdwlYeUPS_PoNGILIq76akuax9QushFNSjMkhFNPfK8zwIcOtpfWIwaacFMRtTTeP6QPb7gzLHqkDdWSa2w/s1600/Screenshot%202022-11-27%20170705.png" width="252" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;br /&gt;&lt;br /&gt;&lt;input id="question11d" name="question11" type="radio" value="d" /&gt;&amp;nbsp;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;b&gt;D)&lt;/b&gt;&amp;nbsp;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGLAOnypn2aMdQrxbgbJag1VqQQlJk8Ns04Wn0cDq5AqzW9wDzvLpDEM_kk5V6hH9JsYvjEcuz6Gb0ZbMRq1yqXIRVBM-09FZe8Pzt8pMN7vvRqeiVJrWpc7eEOlXKx8H0VFkxi-WOpBb7ykGOjmcxi1LJDuhRFCsnNkTSpYA_7a70o-8qkhbXVtMfIg/s249/Screenshot%202022-11-27%20170722.png" style="margin-left: 1em; 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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question" style="text-align: justify;"&gt;&lt;b&gt;12.&amp;nbsp;&lt;/b&gt;&lt;b&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;Consider&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;steady&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;fully&lt;/span&gt;&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;developed&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;flow&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;of&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;a&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;liquid&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;through&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;two&lt;/span&gt;&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;large&lt;/span&gt;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;horizontal&lt;/span&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="letter-spacing: -0.05pt;"&gt;flat&lt;/span&gt;&lt;span style="letter-spacing: -2.7pt;"&gt;&amp;nbsp;&lt;/span&gt;parallel&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;plates&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&amp;nbsp;&lt;/span&gt;separated&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;by&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;a&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;distance&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;2&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;mm.&lt;span style="letter-spacing: -0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;One&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;plate&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;fixed&lt;span style="letter-spacing: -0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;and&lt;span style="letter-spacing: -0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;other plate moves at a speed of 0.5 m/s. What is the magnitude of the&amp;nbsp; &lt;/b&gt;&lt;b&gt;pressure&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;gradient&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;(in&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;Pa/m)&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;in&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;direction&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;flow&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;required&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;to&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;ensure&lt;span style="letter-spacing: -0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;that&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;net&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;flow&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;through&lt;span style="letter-spacing: -0.15pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;plates&lt;span style="letter-spacing: -0.15pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: -0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;zero?&amp;nbsp;&lt;/b&gt;&lt;b&gt;Dynamic&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;viscosity&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;liquid&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;5x10&lt;sup&gt;-4&lt;/sup&gt;&lt;span style="letter-spacing: -0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;Ns/m&lt;sup&gt;2&lt;/sup&gt;&lt;/b&gt;&lt;/div&gt;&lt;p class="TableParagraph" style="margin-top: 0.1pt; text-align: justify;"&gt;&lt;b&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-font-width: 105%;"&gt;(Round&lt;span style="letter-spacing: -0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;off&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;to&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;nearest&lt;span style="letter-spacing: -0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;integer)&amp;nbsp;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/i&gt;&lt;/b&gt;&lt;b&gt;&lt;i&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US;"&gt;&amp;nbsp;[&lt;span style="color: red;"&gt;NAT&lt;/span&gt;]&lt;/span&gt;&lt;/i&gt;&lt;/b&gt;&lt;/p&gt;&lt;ul class="answers"&gt;&lt;br /&gt;&lt;/ul&gt;&lt;style&gt;
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&lt;/style&gt;&lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question12dots"&gt;...&lt;/span&gt;&amp;nbsp;&lt;span id="question12more"&gt;Answer is 374 to 376&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style="color: red;"&gt;&lt;span&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style="color: red;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;button id="question12mybtn" onclick="question12function()"&gt;&lt;b&gt;&lt;span style="color: red;"&gt;Answer&lt;/span&gt;&lt;/b&gt;&lt;/button&gt;&lt;script&gt;
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&lt;/script&gt;&lt;br /&gt;&lt;br /&gt;&lt;div class="question" style="text-align: left;"&gt;&lt;b&gt;13.&amp;nbsp;&lt;/b&gt;&lt;b&gt;For&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;an&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;inviscid&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;fluid&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;with&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;density&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;1&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;kg/m&lt;sup&gt;3&lt;/sup&gt;,&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;Cartesian&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;velocity&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;field&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;is&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;given&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;as:&lt;/b&gt;&lt;/div&gt;&lt;p class="TableParagraph" style="margin-top: 0.1pt; text-align: left;"&gt;&lt;b&gt;&lt;span style="font-size: 11.5pt; mso-bidi-font-size: 11.0pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="font-family: Cambria, &amp;quot;serif&amp;quot;; font-size: 10pt;"&gt;&#119854;&lt;span style="letter-spacing: -0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;=&lt;span style="letter-spacing: 1.15pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;(&lt;/span&gt;—2&#119909;&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;+&lt;span style="letter-spacing: 0.45pt;"&gt;&amp;nbsp;&lt;/span&gt;&#119910;&lt;span style="mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;)&lt;/span&gt;&#119905;&#119842;&lt;span style="letter-spacing: 0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;+&lt;span style="letter-spacing: 0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;span style="mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;(&lt;/span&gt;2&#119909;&lt;span style="letter-spacing: 0.8pt;"&gt;&amp;nbsp;&lt;/span&gt;+&lt;span style="letter-spacing: 0.4pt;"&gt;&amp;nbsp;&lt;/span&gt;&#119910;&lt;span style="mso-text-raise: .5pt; position: relative; top: -0.5pt;"&gt;)&lt;/span&gt;&#119905;&#119843;&lt;span style="letter-spacing: 0.5pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;m/s &lt;/b&gt;&lt;b&gt;Neglecting&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;body&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;forces,&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;find&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;the&lt;span style="letter-spacing: 0.75pt;"&gt;&amp;nbsp;&lt;/span&gt;magnitude&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;of&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;pressure&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;gradient&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;in&lt;span style="letter-spacing: 0.65pt;"&gt;&amp;nbsp;&lt;/span&gt;(Pa/m)&lt;span style="letter-spacing: 0.7pt;"&gt;&amp;nbsp;&lt;/span&gt;at&lt;span style="letter-spacing: -2.6pt;"&gt;&amp;nbsp;&lt;/span&gt;(&lt;i&gt;x,&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;y&lt;/i&gt;)&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;=&lt;span style="letter-spacing: 0.1pt;"&gt;&amp;nbsp;&lt;/span&gt;(1&lt;span style="letter-spacing: 0.2pt;"&gt;&amp;nbsp;&lt;/span&gt;,&lt;span style="letter-spacing: 0.1pt;"&gt;&amp;nbsp;&lt;/span&gt;1)&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;at&lt;span style="letter-spacing: 0.15pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;t&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;=&lt;span style="letter-spacing: 0.15pt;"&gt;&amp;nbsp;&lt;/span&gt;1&lt;span style="letter-spacing: 0.05pt;"&gt;&amp;nbsp;&lt;/span&gt;s.&amp;nbsp;&lt;span style="font-size: 9.5pt; mso-bidi-font-size: 11.0pt;"&gt;&amp;nbsp;&lt;/span&gt;&lt;i&gt;&lt;span style="font-family: &amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; font-size: 11pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US;"&gt;(Round&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;off&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;to&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;two&lt;span style="letter-spacing: 0.6pt;"&gt;&amp;nbsp;&lt;/span&gt;decimal&lt;span style="letter-spacing: 0.55pt;"&gt;&amp;nbsp;&lt;/span&gt;places)&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; &amp;nbsp;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&amp;nbsp; 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&lt;/style&gt;&lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question13dots"&gt;...&lt;/span&gt;&amp;nbsp;&lt;span id="question13more"&gt;Answer is 5.6 to 5.7&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style="color: red;"&gt;&lt;span&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span style="color: red;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;button id="question13mybtn" onclick="question13function()"&gt;&lt;b&gt;&lt;span style="color: red;"&gt;Answer&lt;/span&gt;&lt;/b&gt;&lt;/button&gt;&lt;script&gt;
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&lt;/script&gt;</description><link>https://aerogatetopper.blogspot.com/2022/12/basic-aerodynamics-questions.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/a/AVvXsEibPtM_9eB891iH90RGRSO9Fq9sxmwsKR-9PTi95AIqBsPrDMAXoxSTUkIvry5l9XOYGB1Z8YglFHFyQ3tKAj8IhJFLKw7m9kTKAM3dTaCF9DUKoJTDGtI7SlJ06XMGTm6V6lYPJlKUug962r-fS2HJtVOOvUjqx9Yfd15qOl9YiwT_1wxeTjzMprvWmQ=s72-w400-h191-c" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-1153265559721629250</guid><pubDate>Sun, 22 Aug 2021 06:30:00 +0000</pubDate><atom:updated>2021-08-24T16:52:40.753+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Aptitude and Reasoning</category><title>Aircraft Propulsion s Question and Answer </title><description>&lt;div dir="ltr" style="text-align: left;" trbidi="on"&gt;
&lt;h2 style="text-align: center;"&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111; font-size: large;"&gt;&lt;b&gt;CODING - DECODING MCQ'S QUESTION AND ANSWER&lt;/b&gt;&lt;/span&gt;&lt;/h2&gt;&lt;div&gt;&lt;span style="font-size: large;"&gt;&lt;span style="color: #111111;"&gt;&lt;span style="background-color: white;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span style="font-size: large;"&gt;&lt;span style="color: #111111;"&gt;&lt;span style="background-color: white;"&gt;Coding-decoding type MCQ's questions ask in many different exam like HAL, GOVT. &amp;amp; Technical exams etc. We have collect some types of pattern based question collect for practice.&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;span style="background-color: white; color: #111111;"&gt;Here we will be learn about coding decoding questions.&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111; font-size: large;"&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111; font-size: large;"&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;&lt;div class="question"&gt;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111;"&gt;&lt;b&gt;1. If in a certain code language ‘HOMEWORK‘ is written as ‘KROWEMOH’ . How will ‘PERFECT’ be written in that language?&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;span style="font-size: small;"&gt;&lt;input id="question1a" name="question1" type="radio" value="a" /&gt;&amp;nbsp;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111;"&gt;CTEFREP&lt;/span&gt;&lt;br /&gt;
&lt;input id="question1b" name="question1" type="radio" value="b" /&gt;&amp;nbsp;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111;"&gt;TCEFERP&lt;/span&gt;&lt;br /&gt;
&lt;input id="question1c" name="question1" type="radio" value="c" /&gt;&amp;nbsp;&lt;span face="&amp;quot;Open Sans&amp;quot;, sans-serif" style="background-color: white; color: #111111;"&gt;TCEFRPE&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;input id="question1d" name="question1" type="radio" value="d" /&gt; &lt;label&gt;  TCEFREP &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question1dots"&gt;...&lt;/span&gt;
  &lt;span id="question1more"&gt;Answer is D) &lt;br /&gt;
    TCEFREP&lt;/span&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;2. If in a certain code language ‘SYSTEM’ is written ‘SYSMET’, ‘NEARER’ is written as ‘AENRER’ ,then how ‘FRACTION’ be written in that language?&lt;/b&gt; &lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question2a" name="question2" type="radio" value="a" /&gt; &lt;label&gt;  CARFNOIT &lt;/label&gt; &lt;br /&gt;
&lt;input id="question2b" name="question2" type="radio" value="b" /&gt; &lt;label&gt;  CARFTION&lt;/label&gt; &lt;br /&gt;
&lt;input id="question2c" name="question2" type="radio" value="c" /&gt; &lt;label&gt;  ARFCNOIT &lt;/label&gt; &lt;br /&gt;
&lt;input id="question2d" name="question2" type="radio" value="d" /&gt; &lt;label&gt;  FRACNOIT &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;span style="color: red;"&gt;&lt;b&gt;&lt;span id="question2dots"&gt;...&lt;/span&gt;
  &lt;span id="question2more"&gt;Answer is A) &lt;br /&gt;
CARFNOIT&lt;/span&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;3. If in a certain code language ‘CHOLINE’ is written  as ‘OCIHLEN’, then how will ‘SURGEN’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question3a" name="question3" type="radio" value="a" /&gt; &lt;label&gt;  RSUEGNO &lt;/label&gt; &lt;br /&gt;
&lt;input id="question3b" name="question3" type="radio" value="b" /&gt; &lt;label&gt;  RSEGUNO &lt;/label&gt; &lt;br /&gt;
&lt;input id="question3c" name="question3" type="radio" value="c" /&gt; &lt;label&gt;  RESUGNO &lt;/label&gt; &lt;br /&gt;
&lt;input id="question3d" name="question3" type="radio" value="d" /&gt; &lt;label&gt;  None of these &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question3dots"&gt;...&lt;/span&gt;
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None of these&lt;/span&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;4. If ‘SWAMINATHAN’ is coded as ‘NAHTANIMAWS’ in a certain code language, then how would you code ‘SIGNATURE’ in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question4a" name="question4" type="radio" value="a" /&gt; &lt;label&gt;  ETAGUSNIR &lt;/label&gt; &lt;br /&gt;
&lt;input id="question4b" name="question4" type="radio" value="b" /&gt; &lt;label&gt;  EGUATRNIS &lt;/label&gt; &lt;br /&gt;
&lt;input id="question4c" name="question4" type="radio" value="c" /&gt; &lt;label&gt;  ENGTAURIS &lt;/label&gt; &lt;br /&gt;
&lt;input id="question4d" name="question4" type="radio" value="d" /&gt; &lt;label&gt;  ERUTANGIS &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question4dots"&gt;...&lt;/span&gt;
  &lt;span id="question4more"&gt;Answer is D) &lt;br /&gt;
ERUTANGIS &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;&lt;b&gt;5. In a certain code language ‘BREAKDOWN’ is written as ‘NWODKAERB’ ,then how will ‘TRIANGLES’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question5a" name="question5" type="radio" value="a" /&gt; &lt;label&gt;  SELGNTRIA &lt;/label&gt; &lt;br /&gt;
&lt;input id="question5b" name="question5" type="radio" value="b" /&gt; &lt;label&gt;  AIRTNSELG &lt;/label&gt; &lt;br /&gt;
&lt;input id="question5c" name="question5" type="radio" value="c" /&gt; &lt;label&gt;  SELGNAIRT &lt;/label&gt; &lt;br /&gt;
&lt;input id="question5d" name="question5" type="radio" value="d" /&gt; &lt;label&gt;  AIRTGNSEL &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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#question4more {display: none;}
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question5dots"&gt;...&lt;/span&gt;
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SELGNAIRT &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;&lt;b&gt;6. If in a certain code language ‘BRIGHT’ is written as ‘CSJHIU’,
then how will ‘PUNTER’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question6a" name="question6" type="radio" value="a" /&gt; &lt;label&gt;  QVOUSF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question6b" name="question6" type="radio" value="b" /&gt; &lt;label&gt;  QOVFUS &lt;/label&gt; &lt;br /&gt;
&lt;input id="question6c" name="question6" type="radio" value="c" /&gt; &lt;label&gt;  QVOFUS &lt;/label&gt; &lt;br /&gt;
&lt;input id="question6d" name="question6" type="radio" value="d" /&gt; &lt;label&gt;  QVOUFS &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question6dots"&gt;...&lt;/span&gt;
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QVOUFS &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;7. If in a certain code language ‘COLD’ is written as ‘DPME’, then how will ‘CHINA’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question7a" name="question7" type="radio" value="a" /&gt; &lt;label&gt;  DHIMB &lt;/label&gt; &lt;br /&gt;
&lt;input id="question7b" name="question7" type="radio" value="b" /&gt; &lt;label&gt;  DJKMB &lt;/label&gt; &lt;br /&gt;
&lt;input id="question7c" name="question7" type="radio" value="c" /&gt; &lt;label&gt;  DIJOB &lt;/label&gt; &lt;br /&gt;
&lt;input id="question7d" name="question7" type="radio" value="d" /&gt; &lt;label&gt;  DUPBM &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question7dots"&gt;...&lt;/span&gt;
  &lt;span id="question7more"&gt;Answer is C) &lt;br /&gt;
DIJOB &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;8. If in a certain code language ‘MARCH’ is written as ‘OCTEJ’ then how will ‘RETURN’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question8a" name="question8" type="radio" value="a" /&gt; &lt;label&gt;  TFUVSM &lt;/label&gt; &lt;br /&gt;
&lt;input id="question4b" name="question8" type="radio" value="b" /&gt; &lt;label&gt;  QGSTQM &lt;/label&gt; &lt;br /&gt;
&lt;input id="question8c" name="question8" type="radio" value="c" /&gt; &lt;label&gt;  TGVWTP &lt;/label&gt; &lt;br /&gt;
&lt;input id="question8d" name="question8" type="radio" value="d" /&gt; &lt;label&gt;  TGRVSO &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question8dots"&gt;...&lt;/span&gt;
  &lt;span id="question8more"&gt;Answer is C) &lt;br /&gt;
TGVWTP &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;9. If in a certain code language ‘EARTH’ is written as ‘JVTCG’, then how will ‘GLOBE’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question9a" name="question9" type="radio" value="a" /&gt; &lt;label&gt;  GDQNI &lt;/label&gt; &lt;br /&gt;
&lt;input id="question9b" name="question9" type="radio" value="b" /&gt; &lt;label&gt;  GDQIN &lt;/label&gt; &lt;br /&gt;
&lt;input id="question9c" name="question9" type="radio" value="c" /&gt; &lt;label&gt;  GDNIQ &lt;/label&gt; &lt;br /&gt;
&lt;input id="question9d" name="question9" type="radio" value="d" /&gt; &lt;label&gt;  GDIQN &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question9dots"&gt;...&lt;/span&gt;
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GDQNI &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;&lt;b&gt;10. If in a certain code language ‘BUTTER’ is written as ‘ CVUUFS’
and ‘BREAD’, is written as ‘CSFBE’ then how will ‘ COFFEE’ be written in that code language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question10a" name="question10" type="radio" value="a" /&gt; &lt;label&gt;  DPGGFF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question10b" name="question10" type="radio" value="b" /&gt; &lt;label&gt;  GGDPFF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question10c" name="question10" type="radio" value="c" /&gt; &lt;label&gt;  GDPGFF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question10d" name="question10" type="radio" value="d" /&gt; &lt;label&gt;  FDDPGG &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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DPGGFF &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;11. If ‘HAPPY’ is written as ‘IBQQZ’ in a certain code then how would ‘SORROW’ be written in that code? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question11a" name="question11" type="radio" value="a" /&gt; &lt;label&gt;  TPSSXX &lt;/label&gt; &lt;br /&gt;
&lt;input id="question11b" name="question11" type="radio" value="b" /&gt; &lt;label&gt;  TTPSSPX &lt;/label&gt; &lt;br /&gt;
&lt;input id="question11c" name="question11" type="radio" value="c" /&gt; &lt;label&gt;  TPPSPX &lt;/label&gt; &lt;br /&gt;
&lt;input id="question11d" name="question11" type="radio" value="d" /&gt; &lt;label&gt; None of these &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question11dots"&gt;...&lt;/span&gt;
  &lt;span id="question11more"&gt;Answer is D) &lt;br /&gt;
None of these &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;12. In a certain code ‘RAIN’ is written as ‘TCKP’. How is ‘CLOUD’, written in that code? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question12a" name="question12" type="radio" value="a" /&gt; &lt;label&gt;  ENQWF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question12b" name="question12" type="radio" value="b" /&gt; &lt;label&gt;  EMQWF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question12c" name="question12" type="radio" value="c" /&gt; &lt;label&gt;  FNQWE &lt;/label&gt; &lt;br /&gt;
&lt;input id="question12d" name="question12" type="radio" value="d" /&gt; &lt;label&gt;  ENRWF &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question12dots"&gt;...&lt;/span&gt;
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ENQWF &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;13. If in a certain code language ‘CLUB’ is written as ‘XOFY’, ‘NOT’ is written as ‘MLG’, then will ‘PUNCTUAL’ be written in that code language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question13a" name="question13" type="radio" value="a" /&gt; &lt;label&gt;  KFMGXZFO &lt;/label&gt; &lt;br /&gt;
&lt;input id="question13b" name="question13" type="radio" value="b" /&gt; &lt;label&gt;  KFMXGZFO &lt;/label&gt; &lt;br /&gt;
&lt;input id="question13c" name="question13" type="radio" value="c" /&gt; &lt;label&gt;  KFMXGFZO &lt;/label&gt; &lt;br /&gt;
&lt;input id="question13d" name="question13" type="radio" value="d" /&gt; &lt;label&gt;  KFMXGFOZ &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question13dots"&gt;...&lt;/span&gt;
  &lt;span id="question13more"&gt;Answer is C) &lt;br /&gt;
KFMXGFZO &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;14. If in a certain code language ‘NATURAL’ is written ‘MZGFIZO’, then how will ‘CARE’ be written in that language? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question14a" name="question14" type="radio" value="a" /&gt; &lt;label&gt;  XZIV &lt;/label&gt; &lt;br /&gt;
&lt;input id="question14b" name="question14" type="radio" value="b" /&gt; &lt;label&gt;  XZVI &lt;/label&gt; &lt;br /&gt;
&lt;input id="question14c" name="question14" type="radio" value="c" /&gt; &lt;label&gt;  XVZI &lt;/label&gt; &lt;br /&gt;
&lt;input id="question14d" name="question14" type="radio" value="d" /&gt; &lt;label&gt;  XIZV &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question14dots"&gt;...&lt;/span&gt;
  &lt;span id="question14more"&gt;Answer is A) &lt;br /&gt;
XZIV &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;&lt;b&gt;15. If in a certain code language ‘RASHAMI’ is written as ‘IZHSNR’ then what word will be written for ‘MVVGZ’? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question15a" name="question15" type="radio" value="a" /&gt; &lt;label&gt;  ANDANA &lt;/label&gt; &lt;br /&gt;
&lt;input id="question15b" name="question15" type="radio" value="b" /&gt; &lt;label&gt;  NEETA &lt;/label&gt; &lt;br /&gt;
&lt;input id="question15c" name="question15" type="radio" value="c" /&gt; &lt;label&gt;  ANJALI &lt;/label&gt; &lt;br /&gt;
&lt;input id="question15d" name="question15" type="radio" value="d" /&gt; &lt;label&gt;  POONAM &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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#question15more {display: none;}
&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question15dots"&gt;...&lt;/span&gt;
  &lt;span id="question15more"&gt;Answer is B) &lt;br /&gt;
NEETA &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;
&lt;b&gt;16. If in a certain code language ‘TIGER’ is written as ‘GRTVI’, then what word will be written for ‘HMZPV’? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question16a" name="question16" type="radio" value="a" /&gt; &lt;label&gt;  GREAT &lt;/label&gt; &lt;br /&gt;
&lt;input id="question16b" name="question16" type="radio" value="b" /&gt; &lt;label&gt;  TRACK &lt;/label&gt; &lt;br /&gt;
&lt;input id="question16c" name="question16" type="radio" value="c" /&gt; &lt;label&gt;  PLATE &lt;/label&gt; &lt;br /&gt;
&lt;input id="question16d" name="question16" type="radio" value="d" /&gt; &lt;label&gt;  SNAKE &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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#question16more {display: none;}
&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question16dots"&gt;...&lt;/span&gt;
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SNAKE &lt;/span&gt;&lt;br /&gt;
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  &lt;br /&gt;
&lt;br /&gt;
&lt;div class="question"&gt;&lt;b&gt;17. If in a certain code language ‘LAP’ is coded as ‘KMZBOQ’ then how will ‘NOTE’ be written in that code? &lt;/b&gt;&lt;/div&gt;
&lt;ul class="answers"&gt;

&lt;input id="question17a" name="question17" type="radio" value="a" /&gt; &lt;label&gt;  MONPSUFD &lt;/label&gt; &lt;br /&gt;
&lt;input id="question17b" name="question17" type="radio" value="b" /&gt; &lt;label&gt;  MONPUSDF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question17c" name="question17" type="radio" value="c" /&gt; &lt;label&gt;  MNOPSUDF &lt;/label&gt; &lt;br /&gt;
&lt;input id="question17d" name="question17" type="radio" value="d" /&gt; &lt;label&gt;  MONPSUDF &lt;/label&gt; &lt;br /&gt;

&lt;/ul&gt;
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&lt;/style&gt;
  &lt;b&gt;&lt;span style="color: red;"&gt;&lt;span id="question17dots"&gt;...&lt;/span&gt;
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MONPSUDF &lt;/span&gt;&lt;br /&gt;
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&lt;b&gt;18. If in a certain code language ‘RAM’ is written as ‘QSZBLN’, ‘LOVE’ is written as ‘KMNPUWDF’ . Then how will ‘ACT’ be written as? &lt;/b&gt;&lt;/div&gt;
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&lt;b&gt;19. If in a certain code language ‘REFORM’ is written as ‘426349’ and ‘FORMULA’ is written as ‘6349871’ Then how will ‘MULE’ be written in that language? &lt;/b&gt;&lt;/div&gt;
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&lt;b&gt;20. If in a certain code language ‘GRADUATE’ is written as ‘2092623626722’ then how will ‘ARIHANT’ be written in that language? &lt;/b&gt;&lt;/div&gt;
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&lt;/div&gt;</description><link>https://aerogatetopper.blogspot.com/2021/08/coding-decoding-msqs-question-and-answer.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><thr:total>0</thr:total><georss:featurename>India</georss:featurename><georss:point>20.593684 78.96288</georss:point><georss:box>-7.7165518848024206 43.806627317790984 48.90391988480242 114.11913268220901</georss:box></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-5954477541850481125</guid><pubDate>Mon, 16 Aug 2021 11:39:00 +0000</pubDate><atom:updated>2023-06-03T08:26:55.353+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">aircraft propulsion</category><title>Aircraft Propulsion MCQ's Question and Answer part-1's Question and Answer </title><description>&lt;h2 style="text-align: center;"&gt;&lt;span style="font-size: x-large;"&gt;Aircraft Propulsion Quiz-1&lt;/span&gt;&lt;/h2&gt;&lt;div&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;Here is a quiz to help you prepare your upcoming GATE2022,&amp;nbsp;&lt;a href="https://www.isro.gov.in/" target="_blank"&gt;ISRO&lt;/a&gt;,&amp;nbsp;&lt;a href="https://hal-india.co.in/" target="_blank"&gt;HAL&lt;/a&gt;&amp;nbsp;exam. The GATE AE paper has several subjects, each one is equally important. However, one of the most important subjects in GATE AE is Aircraft Propulsion. The subject is vast, but practice makes tackling it easy. Few questions are like same but there is a minute difference between them so it will also increase the thinking ability of the students.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;This quiz contains important questions which match the pattern of the GATE, ISRO &amp;amp; HAL exams. Check your preparation level in every chapter of Aircraft Propulsion for GATE by taking the quiz and comparing your ranks. Learn about Gas turbine engine, Engine performance, Engine components and more!&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://aerogatetopper.blogspot.com/p/gate-2022.html" style="margin-left: 1em; margin-right: 1em;" target="_blank"&gt;&lt;img alt="Aircraft Propulsion mock test" border="0" data-original-height="600" data-original-width="1067" height="380" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDJhIirza5pdmLwoAAFrcIj7CWpDdAcc1aEX-tcJgvYNL4Xtm3XxJCv6zaIVO0ZJUXD5mNlhi6xLODe7gYnOnI3xIX8mR37-ajL-Qgnsiexo0HWJA4XlqGxG6QVxtQagDG8K4eXY1alyax/w584-h380/earth-7680x4320-planet-space-10121.jpg" title="Aircraft Propulsion mock test" width="584" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;span style="font-size: x-large;"&gt;&lt;p style="text-align: justify;"&gt;&lt;span&gt;To know whether you have achieved the required preparation or test your time management as per the question pattern within an exam environment, join these mock test.&lt;/span&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span&gt;
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&lt;/script&gt;</description><link>https://aerogatetopper.blogspot.com/2021/08/aircraft-propulsion-mcqs-question-and-answer.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDJhIirza5pdmLwoAAFrcIj7CWpDdAcc1aEX-tcJgvYNL4Xtm3XxJCv6zaIVO0ZJUXD5mNlhi6xLODe7gYnOnI3xIX8mR37-ajL-Qgnsiexo0HWJA4XlqGxG6QVxtQagDG8K4eXY1alyax/s72-w584-h380-c/earth-7680x4320-planet-space-10121.jpg" width="72"/><thr:total>0</thr:total><georss:featurename>India</georss:featurename><georss:point>20.593684 78.96288</georss:point><georss:box>-7.7165518848024206 43.806627317790984 48.90391988480242 114.11913268220901</georss:box></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-6210432293018987098</guid><pubDate>Sun, 18 Jul 2021 08:49:00 +0000</pubDate><atom:updated>2021-07-19T21:34:25.729+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">aerodynamics mock test</category><title>Aerodynamics [MCQs] Mock Test-3 for GATE Aerospace-2022 by AERO GATE TOPPER</title><description>&lt;h1 style="text-align: center;"&gt;&lt;span style="background-color: #f1c232;"&gt;&amp;nbsp;Aerodynamics&amp;nbsp;&lt;/span&gt;&lt;/h1&gt;&lt;p&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;Here is a quiz to help you prepare your upcoming GATE2022,&amp;nbsp;&lt;a href="https://www.isro.gov.in/" target="_blank"&gt;ISRO&lt;/a&gt;,&amp;nbsp;&lt;a href="https://hal-india.co.in/" target="_blank"&gt;HAL&lt;/a&gt;&amp;nbsp;exam. The GATE AE paper has several subjects, each one is equally important. However, one of the most important subjects in GATE AE is Aerodynamics. The subject is vast, but practice makes tackling it easy.Few questions are like same but there is a minute difference between them so it will also increase the thinking ability of the students.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;This quiz contains important questions which match the pattern of the GATE, ISRO &amp;amp; HAL exams. Check your preparation level in every chapter of Aerodynamics for GATE by taking the quiz and comparing your ranks. Learn about Pitot tube, basics of aerodynamics and more!&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;&lt;span&gt;To know whether you have achieved the required preparation or test your time management as per the question pattern within an exam environment, join these mock test.&lt;/span&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;br /&gt;&lt;/div&gt;&lt;h3 style="clear: both; text-align: center;"&gt;&lt;div class="separator" style="clear: both;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAb0ZGdHnk8ZgfeyRIwqZs_e2m355FLtiDCPJO6FZjEePhiXjwYQQTwhq6Y2oYMr9tqCo4ce0aS_eZb6srYv2DbxYpQc5logpmoPumcZLqg32uiKuqHeASgNEn_zDLLPkVVcw4zm0x_hs/s281/download.png" style="display: block; padding: 1em 0px; text-align: center;"&gt;&lt;img alt="" border="0" data-original-height="179" data-original-width="281" height="254" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAb0ZGdHnk8ZgfeyRIwqZs_e2m355FLtiDCPJO6FZjEePhiXjwYQQTwhq6Y2oYMr9tqCo4ce0aS_eZb6srYv2DbxYpQc5logpmoPumcZLqg32uiKuqHeASgNEn_zDLLPkVVcw4zm0x_hs/w400-h254/download.png" width="400" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;b&gt;&lt;span style="color: #38761d; font-size: x-large;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/h3&gt;&lt;h3 style="clear: both; text-align: center;"&gt;&lt;b&gt;&lt;span style="color: #38761d; font-size: x-large;"&gt;Aerodynamics Mock test 3&lt;/span&gt;&lt;/b&gt;&lt;/h3&gt;
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&lt;script src="https://uquiz.com/embed.js"&gt;&lt;/script&gt;</description><link>https://aerogatetopper.blogspot.com/2021/07/Aerodynamics-MCQs-Mock-Test-3-for-GATE-Aerospace-2022-by-AERO-GATE-TOPPER.html</link><author>noreply@blogger.com (Unknown)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAb0ZGdHnk8ZgfeyRIwqZs_e2m355FLtiDCPJO6FZjEePhiXjwYQQTwhq6Y2oYMr9tqCo4ce0aS_eZb6srYv2DbxYpQc5logpmoPumcZLqg32uiKuqHeASgNEn_zDLLPkVVcw4zm0x_hs/s72-w400-h254-c/download.png" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-7509066006923488159</guid><pubDate>Sun, 18 Jul 2021 07:55:00 +0000</pubDate><atom:updated>2021-07-19T21:33:32.937+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">aerodynamics mock test</category><title>Aerodynamics [MCQs] Mock Test-2 for GATE Aerospace-2022 by AERO GATE TOPPER</title><description>
&lt;h1 style="text-align: center;"&gt;&lt;span style="background-color: #f1c232;"&gt;&amp;nbsp;Aerodynamics&amp;nbsp;&lt;/span&gt;&lt;/h1&gt;&lt;p&gt;&lt;br /&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;Here is a quiz to help you prepare for your upcoming GATE aerospace 2022,&amp;nbsp;&lt;a href="https://www.isro.gov.in/" target="_blank"&gt;ISRO&lt;/a&gt;,&amp;nbsp;&lt;a href="https://hal-india.co.in/" target="_blank"&gt;HAL&lt;/a&gt;&amp;nbsp;exam. The GATE AE paper has several subjects, each one is equally important. However, one of the most important subjects in GATE AE is Aerodynamics. The subject is vast, but practice makes tackling it easy. AERO GATE TOPPER is the place where you will be able to grow your knowledge by attempting the test series of different level of questions.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;This quiz contains important questions which match the pattern of the GATE, ISRO &amp;amp; HAL exams. Check your preparation level in every chapter of Aerodynamics for GATE by taking the quiz and comparing your ranks. Learn about Pitot tube, Coefficient of lift drag &amp;amp; moments as well as different topics related to aerodynamics basics of aerodynamics as well as higher level of aerodynamics!&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;&lt;span&gt;To know whether you have achieved the required preparation or test your time manag&lt;/span&gt;&lt;/span&gt;&lt;span style="font-size: x-large; text-align: left;"&gt;ement as per the question pattern within an exam environment, join these mock test.&lt;/span&gt;&lt;/p&gt;&lt;span style="font-size: large;"&gt;&lt;span&gt;&lt;span&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglygX-VZGYBED3Qvb54VQh9x_oCbjFbLGxmP8_1o9DHR-c9l97Ocg0cGxeC4FguMr7wDkljlCso1-VBs2yNuz-6W7aGSf40irLnCybqFpq1gX4UqzusB0TtBOH2J1WXR8Az0aeBTEw4l8/s1372/12108828_1512780695700184_996571587550772773_n.jpg" style="display: block; padding: 1em 0px; text-align: center;"&gt;&lt;img alt="" border="0" data-original-height="768" data-original-width="1372" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglygX-VZGYBED3Qvb54VQh9x_oCbjFbLGxmP8_1o9DHR-c9l97Ocg0cGxeC4FguMr7wDkljlCso1-VBs2yNuz-6W7aGSf40irLnCybqFpq1gX4UqzusB0TtBOH2J1WXR8Az0aeBTEw4l8/w476-h266/12108828_1512780695700184_996571587550772773_n.jpg" width="476" /&gt;&lt;/a&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;h3 style="clear: both; text-align: center;"&gt;&lt;b&gt;&lt;span style="color: #38761d; font-size: x-large;"&gt;Aerodynamics Mock test 2&lt;/span&gt;&lt;/b&gt;&lt;/h3&gt;&lt;div data-quiz-id="bbhksa" data-width="100%" id="uquiz_embed"&gt;&lt;/div&gt;
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</description><link>https://aerogatetopper.blogspot.com/2021/07/Aerodynamics-MCQs-Mock-Test-2-for-GATE-Aerospace-2022-by-AERO-GATE-TOPPER.html</link><author>noreply@blogger.com (Unknown)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglygX-VZGYBED3Qvb54VQh9x_oCbjFbLGxmP8_1o9DHR-c9l97Ocg0cGxeC4FguMr7wDkljlCso1-VBs2yNuz-6W7aGSf40irLnCybqFpq1gX4UqzusB0TtBOH2J1WXR8Az0aeBTEw4l8/s72-w476-h266-c/12108828_1512780695700184_996571587550772773_n.jpg" width="72"/><thr:total>0</thr:total><georss:featurename>India</georss:featurename><georss:point>20.593684 78.96288</georss:point><georss:box>-7.715500937427084 43.808003291015623 48.902868937427087 114.11775670898437</georss:box></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-6707587682853355533</guid><pubDate>Sat, 03 Jul 2021 00:30:00 +0000</pubDate><atom:updated>2023-06-03T08:36:24.582+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Basic</category><title>Importance of the test series entrance exam preparation</title><description>&lt;h2 style="text-align: left;"&gt;&amp;nbsp;Why test series?&lt;/h2&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;Test or examination plays a very vital role while you are preparing for any type of exams weather they are competitive or sessional. By the help of tests students can check their ability that how much they are ready to conquer the sky? Also by the help of test they can check their marks and can improve themselves for further exams. In competitive exams test series plays a good role to find out their mistakes as well as time duration for each test. Students who are feeling nervous during the examination because of lake practice so this test is also beneficial for them.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidDTjOALDeZv3RcUgNkxhTrYOWuABW5duodwk1i2M315Z0oa1PuHXDibU7seSfurX7Na-83nie8NjTHV4bAGsHMXMbxEyPPyqmeR_G2iATB5770PAlv9ru1TLLGsL3JP_8JJSXdHZq2z8d/s619/Why+test+series.jpg" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;img alt="Why test series" border="0" data-original-height="347" data-original-width="619" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidDTjOALDeZv3RcUgNkxhTrYOWuABW5duodwk1i2M315Z0oa1PuHXDibU7seSfurX7Na-83nie8NjTHV4bAGsHMXMbxEyPPyqmeR_G2iATB5770PAlv9ru1TLLGsL3JP_8JJSXdHZq2z8d/w400-h224/Why+test+series.jpg" title="Why test series" width="400" /&gt;&lt;/a&gt;&lt;/div&gt;&lt;br /&gt;&lt;span style="font-size: large;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;p&gt;&lt;/p&gt;&lt;h2 style="text-align: left;"&gt;Optimize your loading time&lt;/h2&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;This quiz contains important questions which match the pattern of the GATE, ISRO &amp;amp; HAL exams. Check your preparation level in every chapter wise for GATE by taking the quiz and comparing your ranks.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;To know whether you have achieved the required preparation or test your time management as per the question pattern within an exam environment, join these mock test.&amp;nbsp;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p style="text-align: justify;"&gt;&lt;span style="font-size: large;"&gt;&lt;script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-2922315402866630"
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&lt;/script&gt;&lt;/span&gt;&lt;/p&gt;</description><link>https://aerogatetopper.blogspot.com/2021/07/importance-of-test-series-entrance-exam.html</link><author>noreply@blogger.com (AERO GATE TOPPER)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidDTjOALDeZv3RcUgNkxhTrYOWuABW5duodwk1i2M315Z0oa1PuHXDibU7seSfurX7Na-83nie8NjTHV4bAGsHMXMbxEyPPyqmeR_G2iATB5770PAlv9ru1TLLGsL3JP_8JJSXdHZq2z8d/s72-w400-h224-c/Why+test+series.jpg" width="72"/><thr:total>0</thr:total><georss:featurename>India</georss:featurename><georss:point>20.593684 78.96288</georss:point><georss:box>-10.835811034471067 43.80663 52.02317903447107 114.11913</georss:box></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-7019986798556737606</guid><pubDate>Fri, 02 Jul 2021 12:18:00 +0000</pubDate><atom:updated>2022-11-12T14:06:07.103+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Aircraft Structure</category><title>Characteristics of aircraft Structure</title><description>&lt;h2&gt;&lt;strong&gt;Characteristics of aircraft Structure:-&lt;/strong&gt;&lt;/h2&gt;&lt;ul&gt;&lt;li&gt;Marine aircraft are built to meet certain specified requirements. These requirements must be selected so they can be built into one aircraft.&lt;/li&gt;&lt;li&gt;One aircraft can't possess all characteristics; just as an aircraft can't have the comfort of passenger transport and the maneuverability of a fighter.&lt;/li&gt;&lt;li&gt;Each type of aircraft determines however strong it should be built.&lt;/li&gt;&lt;li&gt;The Navy fighter should be quick, maneuverable(well controlled), and equipped for attack and defend. To satisfy these requirements, the aircraft is extremely powerful and features a very strong structure.&lt;/li&gt;&lt;/ul&gt;&lt;p&gt;&lt;strong&gt;The airframe of a fixed-wing aircraft consists of the following five major units&lt;/strong&gt;:&lt;/p&gt;&lt;ol&gt;&lt;li&gt;Fuselage&lt;/li&gt;&lt;li&gt;Wings&lt;/li&gt;&lt;li&gt;Stabilizers&lt;/li&gt;&lt;li&gt;Flight controls surfaces&lt;/li&gt;&lt;li&gt;Landing gear&lt;/li&gt;&lt;/ol&gt;&lt;p&gt;&lt;strong&gt;A rotary-wing aircraft consists of the following four major units&lt;/strong&gt;:&lt;/p&gt;&lt;ol&gt;&lt;li&gt;Fuselage&lt;/li&gt;&lt;li&gt;Landing gear&lt;/li&gt;&lt;li&gt;Main rotor assembly&lt;/li&gt;&lt;li&gt;Tail rotor assembly&lt;/li&gt;&lt;/ol&gt;&lt;p&gt;&lt;strong&gt;&amp;nbsp;&lt;/strong&gt;&lt;/p&gt;&lt;h2&gt;&lt;strong&gt;Construction of aircraft:-&lt;table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td style="text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxkFtM14CgrsUsaaQ4-mZ7gGiMc6uYQr5krzWp7Gd2FyPxlHxeC69nnulfkbYSF-_ExKrptZm3A82zcR0rMpXTjk7AOVL-KpQ3M4G7eNC2p0wtkelruZyGZzmDZwNa2e8jclL9yO6agA/s469/Parts-of-an-aircraft-and+their-function.png" style="margin-left: auto; margin-right: auto;"&gt;&lt;img alt="parts of an aircraft &amp;amp; their functions, aircraft components" border="0" data-original-height="362" data-original-width="469" height="551" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxkFtM14CgrsUsaaQ4-mZ7gGiMc6uYQr5krzWp7Gd2FyPxlHxeC69nnulfkbYSF-_ExKrptZm3A82zcR0rMpXTjk7AOVL-KpQ3M4G7eNC2p0wtkelruZyGZzmDZwNa2e8jclL9yO6agA/w694-h551/Parts-of-an-aircraft-and+their-function.png" title="parts of an aircraft &amp;amp; their functions" width="694" /&gt;&lt;/a&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="tr-caption" style="text-align: center;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Components of an aircraft &amp;amp; their functions&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/strong&gt;&lt;/h2&gt;&lt;h3&gt;&lt;strong&gt;Working of Airframe:-&lt;/strong&gt;&lt;/h3&gt;&lt;h3&gt;&lt;strong&gt;FUSELAGE:-&lt;/strong&gt;&lt;/h3&gt;&lt;p&gt;A fuselage is the main structure, or body, of the aircraft. It provides space for staff, cargo, controls, and most of the accessories. The power plant, wings, stabilizers, and landing gear are included.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;There are two general types of fuselage construction—&lt;/strong&gt;&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;1. Monocoque:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;The &lt;strong&gt;true monocoque&lt;/strong&gt; construction uses formers, frame assemblies, and bulkheads to create a fuselage structure. However, the skin carries the primary stresses/pressures. Since no bracing members are present, the skin ought to be strong enough to keep the fuselage rigid. The biggest problem in monocoque construction is maintaining enough strength while keeping the weight within limits.&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;2. Semi monocoque:-&lt;/strong&gt;&lt;/h4&gt;&lt;ul&gt;&lt;li&gt;Semi monocoque design overcomes the strength-to-weight problem of monocoque construction. In addition to having designers, frame assemblies, and bulkheads, the semi-monocoque structure has the skin strengthened by longitudinal members.&lt;/li&gt;&lt;li&gt;An aircraft should be constructed of materials that are each lightweight and strong. Early aircraft were made of wood. Lightweight metal alloys with greater strength than wood are developed and used in the latest aircraft.&lt;/li&gt;&lt;/ul&gt;&lt;h3&gt;&lt;strong&gt;WINGS:-&lt;/strong&gt;&lt;/h3&gt;&lt;p&gt;Wings develop the major portion of the lift of a heavier-than-air aircraft. The wing structures carry some of the heavier loads found in the aircraft structure. The particular design of a wing depends on many factors, such as the size, weight, speed, rate of climb, and use of the aircraft.&lt;/p&gt;&lt;h3&gt;&lt;strong&gt;STABILIZERS:-&lt;/strong&gt;&lt;/h3&gt;&lt;p&gt;The stabilizing surfaces of aircraft carries with it vertical and horizontal airfoils. They are known as the vertical stabilizer (or fin) and horizontal stabilizer. These 2 airfoils, beside the rudder and elevators, type a part of the tail section. For inspection and maintenance purposes, the entire tail section is considered a single unit called the empennage.&lt;/p&gt;&lt;h3&gt;&lt;strong&gt;LANDING GEAR:-&lt;br /&gt;&lt;/strong&gt;&lt;/h3&gt;&lt;p&gt;It is the framing of an aircraft or spacecraft and can be used for either takeoff or &lt;strong&gt;&lt;em&gt;landing&lt;/em&gt;&lt;/strong&gt;. For aircraft, it is generally needed for both. It was also formerly called alighting&amp;nbsp;&lt;strong&gt;&lt;em&gt;gear &lt;/em&gt;&lt;/strong&gt;by some manufacturers.&lt;/p&gt;&lt;table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td style="text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCulM9H3ISL0Xd4Y25udWL_NJKJQkbDkRRgx2eSHwXVWCCWxk9jZo_1xxm68ouURYo9DDEz-fyupRzsey0Ok30LgHg0JJqtZPfl4CL00j3z9eWHooou9_7fkecq9P5VxlDlgKMJXfdsQ/s850/Landing-gear-a-Multibody-model-b-main-structural-components.png" style="margin-left: auto; margin-right: auto;"&gt;&lt;img alt="landing gear, landing gear of an aircraft" border="0" data-original-height="587" data-original-width="850" height="509" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCulM9H3ISL0Xd4Y25udWL_NJKJQkbDkRRgx2eSHwXVWCCWxk9jZo_1xxm68ouURYo9DDEz-fyupRzsey0Ok30LgHg0JJqtZPfl4CL00j3z9eWHooou9_7fkecq9P5VxlDlgKMJXfdsQ/w584-h509/Landing-gear-a-Multibody-model-b-main-structural-components.png" title="Landing gear" width="584" /&gt;&lt;/a&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="tr-caption" style="text-align: center;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Landing-gear-(a)Multibody-model (b)main structural components&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;h2&gt;&lt;strong&gt;&lt;br /&gt;Aircraft Materials&lt;/strong&gt;:-&lt;/h2&gt;&lt;p&gt;Currently used in aircraft construction of aircraft are classified as either metallic materials or non-metallic material.&lt;/p&gt;&lt;p&gt;&amp;nbsp;&lt;/p&gt;&lt;table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td style="text-align: center;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuxbwZiokax9SJgs7rAIX1dcF3jJmNXgab9LWPGUeTbNwEMgUa24J-PDs44WHTnzUMnPz_X5jDN1RfLtpc6ujUXYIFE6T-0rmBuLdIVDYd0JGgcRUzBzmZfiRdO2y7YFNNbMP7cepsaA/s2048/Composite-materials-in-aircraft.png" style="margin-left: auto; margin-right: auto;"&gt;&lt;img alt="composite materials in aircraft component, composite materials" border="0" data-original-height="1481" data-original-width="2048" height="570" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuxbwZiokax9SJgs7rAIX1dcF3jJmNXgab9LWPGUeTbNwEMgUa24J-PDs44WHTnzUMnPz_X5jDN1RfLtpc6ujUXYIFE6T-0rmBuLdIVDYd0JGgcRUzBzmZfiRdO2y7YFNNbMP7cepsaA/w706-h570/Composite-materials-in-aircraft.png" title="composite materials in aircraft component" width="706" /&gt;&lt;/a&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="tr-caption" style="text-align: center;"&gt;&lt;b&gt;&lt;span style="font-size: medium;"&gt;Composite materials in aircraft component&lt;/span&gt;&lt;/b&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;br /&gt;&lt;p&gt;&lt;/p&gt;&lt;h3&gt;&lt;strong&gt;METALLIC MATERIALS:-&lt;/strong&gt;&lt;/h3&gt;&lt;p&gt;The most common metals used in aircraft construction are aluminum, magnesium, titanium, steel, and their alloys.&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;Alloys:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Alloy is made of two or more metals. The metal present in the alloy in the largest amount is called the &lt;strong&gt;base metal&lt;/strong&gt;.&lt;/p&gt;&lt;ul&gt;&lt;li&gt;All alternative metals added to the base metal are called alloying parts. Adding the alloying components could end in a modification within the properties of the base metal.&lt;/li&gt;&lt;li&gt;For example, pure aluminum is comparatively soft and weak. However, adding tiny amounts of copper, manganese, and magnesium can usually increase the strength of aluminum many times.&lt;/li&gt;&lt;li&gt;Heat treatment can increase or decrease the strength and hardness of the alloy.&lt;/li&gt;&lt;li&gt;Alloys are important to the aircraft industry. They provide building materials with properties that pure metals don't possess.&lt;/li&gt;&lt;/ul&gt;&lt;h4&gt;&lt;strong&gt;Aluminum:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Aluminum alloys are widely used in the construction of modern aircraft. Its alloys are important because they have a high strength-to-weight ratio. Aluminum alloys are resistant to corrosion and comparatively easy to fabricate. An outstanding characteristic of aluminum is its lightweight.&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;Magnesium:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Magnesium is the lightest metal in the world. It is a silvery-white material that weighs two-thirds as much as aluminum. Magnesium is used to make helicopters. Magnesium's low resistance to corrosion and corrosion has reduced its use in conventional aircraft.&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;Titanium:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Titanium is a lightweight, strong, corrosion-resistant metal. Recent developments make titanium ideal for applications where aluminum alloys are too weak and stainless steel is too heavy. Additionally, titanium is unaffected by long exposure to seawater and the ocean-atmosphere (the marine atmosphere).&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;Steel Alloys:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Alloy steels used in aircraft construction have great strength, more so than other fields of engineering would require. These materials should withstand the forces that occur from modern aircraft. These steels contain small percentages of carbon, nickel, chromium, vanadium, and molybdenum. High-tensile steels will stand the stress of 50 to 150 tons per square inch without fail. Such instruments are made of tubes, rods, and wires. Another type of steel used is stainless steel. Stainless steel resistant to corrosion and is particularly important for use in or near water.&lt;/p&gt;&lt;h3&gt;&lt;strong&gt;NONMETALLIC MATERIALS&lt;/strong&gt;&lt;strong&gt;:-&lt;/strong&gt;&lt;/h3&gt;&lt;p&gt;In addition to metals, various types of plastic materials are found in aircraft construction. Some of these plastics include transparent plastic, reinforced plastic, composite materials, and carbon-fiber materials.&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;Transparent Plastic:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Transparent plastic is used in canopies, windshields (front window), and alternative transparent enclosures. You would like to handle transparent plastic surfaces carefully as a result of they're relatively soft and simply scratched. At approximately 225°F, transparent plastic becomes soft and flexible.&lt;/p&gt;&lt;h4&gt;&lt;strong&gt;Reinforced Plastic:-&lt;/strong&gt;&lt;/h4&gt;&lt;p&gt;Reinforced plastic is used in the construction of radomes, wingtips, stabilizer tips, antenna covers, and flight controls. It has a high strength-to-weight ratio and is resistant to mildew and rot. Because it is easy to fabricate. it is equally suitable for other parts of the aircraft. Reinforced plastic is a sandwich-type material. It is made up of two outer facings and a center layer.&lt;/p&gt;</description><link>https://aerogatetopper.blogspot.com/2021/05/characteristics-of-aircraft-structure_24.html</link><author>noreply@blogger.com (Unknown)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxkFtM14CgrsUsaaQ4-mZ7gGiMc6uYQr5krzWp7Gd2FyPxlHxeC69nnulfkbYSF-_ExKrptZm3A82zcR0rMpXTjk7AOVL-KpQ3M4G7eNC2p0wtkelruZyGZzmDZwNa2e8jclL9yO6agA/s72-w694-h551-c/Parts-of-an-aircraft-and+their-function.png" width="72"/><thr:total>0</thr:total></item><item><guid isPermaLink="false">tag:blogger.com,1999:blog-7829887098258372846.post-6143313630650573483</guid><pubDate>Fri, 02 Jul 2021 10:55:00 +0000</pubDate><atom:updated>2022-11-12T14:06:09.849+05:30</atom:updated><category domain="http://www.blogger.com/atom/ns#">Space dynamics</category><title>Types of Orbits</title><description>&lt;p&gt;&lt;br /&gt;&lt;/p&gt; &lt;p class="PadderBetweenControlandBody"&gt;&lt;o:p&gt;&amp;nbsp;&lt;/o:p&gt;&lt;/p&gt;  &lt;p class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo1; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"&gt;&lt;span style="mso-list: Ignore;"&gt;1.&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;Geostationary Orbit&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;T= 24 hours&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Circular orbit&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l0 level1 lfo2; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Inclination angle 0&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"&gt;°&lt;/span&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l1 level1 lfo1; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"&gt;&lt;span style="mso-list: Ignore;"&gt;2.&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;Geosynchronous Orbit [GEO]&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l4 level1 lfo3; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;T= 24 hours&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l4 level1 lfo3; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Inclination other than 0&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"&gt;°&lt;/span&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l4 level1 lfo3; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Height of such a satellite is given by:&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0in; mso-add-space: auto;"&gt;&lt;!--[if gte msEquation 12]&gt;&lt;m:oMathPara&gt;&lt;m:oMath&gt;&lt;i   style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;   font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;h&lt;/m:r&gt;&lt;m:r&gt;=&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;m:sSup&gt;&lt;m:sSupPr&gt;&lt;span     style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:12.0pt;     font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";     mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:     normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:sSupPr&gt;&lt;m:e&gt;&lt;m:d&gt;&lt;m:dPr&gt;&lt;span       style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:       12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:       normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:dPr&gt;&lt;m:e&gt;&lt;m:f&gt;&lt;m:fPr&gt;&lt;span         style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:         12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";         mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;         mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:         normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:fPr&gt;&lt;m:num&gt;&lt;i         style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;         font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;g&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;m:sSup&gt;&lt;m:sSupPr&gt;&lt;span           style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:           12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";           mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;           mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:           normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:sSupPr&gt;&lt;m:e&gt;&lt;i           style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt; 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          font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;2&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:sup&gt;&lt;/m:sSup&gt;&lt;/m:num&gt;&lt;m:den&gt;&lt;i         style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;         font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;4&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;m:sSup&gt;&lt;m:sSupPr&gt;&lt;span           style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:           12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";           mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;           mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:           normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:sSupPr&gt;&lt;m:e&gt;&lt;i           style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;           font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;π&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:e&gt;&lt;m:sup&gt;&lt;i           style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;           font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;2&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:sup&gt;&lt;/m:sSup&gt;&lt;/m:den&gt;&lt;/m:f&gt;&lt;/m:e&gt;&lt;/m:d&gt;&lt;/m:e&gt;&lt;m:sup&gt;&lt;m:f&gt;&lt;m:fPr&gt;&lt;span       style='font-size:12.0pt;mso-ansi-font-size:12.0pt;mso-bidi-font-size:       12.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";       mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:       normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:fPr&gt;&lt;m:num&gt;&lt;i       style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;       font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;1&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:num&gt;&lt;m:den&gt;&lt;i       style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;       font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;3&lt;span        style='mso-spacerun:yes'&gt;  &lt;/span&gt;&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:den&gt;&lt;/m:f&gt;&lt;/m:sup&gt;&lt;/m:sSup&gt;&lt;i   style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='font-size:12.0pt;   font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;-&lt;/m:r&gt;&lt;m:r&gt;R&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:oMath&gt;&lt;/m:oMathPara&gt;&lt;![endif]--&gt;&lt;!--[if !msEquation]--&gt;&lt;span face="&amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;" style="font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shapetype  id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"  path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"&gt; &lt;v:stroke joinstyle="miter"/&gt; &lt;v:formulas&gt;  &lt;v:f eqn="if lineDrawn pixelLineWidth 0"/&gt;  &lt;v:f eqn="sum @0 1 0"/&gt;  &lt;v:f eqn="sum 0 0 @1"/&gt;  &lt;v:f eqn="prod @2 1 2"/&gt;  &lt;v:f eqn="prod @3 21600 pixelWidth"/&gt;  &lt;v:f eqn="prod @3 21600 pixelHeight"/&gt;  &lt;v:f eqn="sum @0 0 1"/&gt;  &lt;v:f eqn="prod @6 1 2"/&gt;  &lt;v:f eqn="prod @7 21600 pixelWidth"/&gt;  &lt;v:f eqn="sum @8 21600 0"/&gt;  &lt;v:f eqn="prod @7 21600 pixelHeight"/&gt;  &lt;v:f eqn="sum @10 21600 0"/&gt; &lt;/v:formulas&gt; &lt;v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/&gt; &lt;o:lock v:ext="edit" aspectratio="t"/&gt;&lt;/v:shapetype&gt;&lt;v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:102pt;  height:39.75pt'&gt; &lt;v:imagedata src="file:///C:\Users\mohit\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"   o:title="" chromakey="white"/&gt;&lt;/v:shape&gt;&lt;![endif]--&gt;&lt;/span&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;span face="&amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;" style="font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhi69uKmddljfPudBbZu1DfWJljn0-THp0vEw0FA3VMLCFY46KT3FJY1TURPnNQdItGGqSuxfxqPS_3wc-urlxjQYWkHLvmUi9VbABRaH43JXzqwF-EP8glOU-K9fxhwU3TUf1jup3X9Q/" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;img alt="" data-original-height="184" data-original-width="467" height="87" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhi69uKmddljfPudBbZu1DfWJljn0-THp0vEw0FA3VMLCFY46KT3FJY1TURPnNQdItGGqSuxfxqPS_3wc-urlxjQYWkHLvmUi9VbABRaH43JXzqwF-EP8glOU-K9fxhwU3TUf1jup3X9Q/w219-h87/image.png" width="219" /&gt;&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;&lt;span face="&amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;" style="font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;sub&gt;&lt;span style="font-size: 12pt;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/sub&gt;&lt;p&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0in; mso-add-space: auto; text-indent: 1.25in;"&gt;&lt;sub&gt;&lt;span style="font-size: 14pt;"&gt;&lt;span style="mso-spacerun: yes;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;h=36,000Km&lt;/span&gt;&lt;/sub&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="font-size: 14pt;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l4 level1 lfo3; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;The orbit in which geostationary satellite revolves is called &lt;b style="mso-bidi-font-weight: normal;"&gt;parking orbit.&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l4 level1 lfo3; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Orbital velocity of such satellite,&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0in; mso-add-space: auto;"&gt;&lt;!--[if gte msEquation 12]&gt;&lt;m:oMathPara&gt;&lt;m:oMath&gt;&lt;i   style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:11.0pt;   font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;V&lt;/m:r&gt;&lt;m:r&gt;=&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;m:rad&gt;&lt;m:radPr&gt;&lt;m:degHide      m:val="on"/&gt;&lt;span style='mso-bidi-font-size:11.0pt;font-family:"Cambria Math","serif";     mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:Calibri;     mso-fareast-theme-font:minor-latin;mso-hansi-font-family:"Cambria Math";     font-style:italic;mso-bidi-font-style:normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:radPr&gt;&lt;m:deg&gt;&lt;/m:deg&gt;&lt;m:e&gt;&lt;m:f&gt;&lt;m:fPr&gt;&lt;span       style='mso-bidi-font-size:11.0pt;font-family:"Cambria Math","serif";       mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:Calibri;       mso-fareast-theme-font:minor-latin;mso-hansi-font-family:"Cambria Math";       font-style:italic;mso-bidi-font-style:normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:fPr&gt;&lt;m:num&gt;&lt;i       style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:       11.0pt;font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;g&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;m:sSup&gt;&lt;m:sSupPr&gt;&lt;span         style='mso-bidi-font-size:11.0pt;font-family:"Cambria Math","serif";         mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:Calibri;         mso-fareast-theme-font:minor-latin;mso-hansi-font-family:"Cambria Math";         font-style:italic;mso-bidi-font-style:normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:sSupPr&gt;&lt;m:e&gt;&lt;i         style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:         11.0pt;font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;R&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:e&gt;&lt;m:sup&gt;&lt;i         style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:         11.0pt;font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;2&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:sup&gt;&lt;/m:sSup&gt;&lt;/m:num&gt;&lt;m:den&gt;&lt;i       style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:       11.0pt;font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;R&lt;/m:r&gt;&lt;m:r&gt;+h&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:den&gt;&lt;/m:f&gt;&lt;/m:e&gt;&lt;/m:rad&gt;&lt;i   style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:11.0pt;   font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;=3.1&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;m:f&gt;&lt;m:fPr&gt;&lt;m:type      m:val="skw"/&gt;&lt;span style='mso-bidi-font-size:11.0pt;font-family:"Cambria Math","serif";     mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:Calibri;     mso-fareast-theme-font:minor-latin;mso-hansi-font-family:"Cambria Math";     font-style:italic;mso-bidi-font-style:normal;vertical-align:sub'&gt;&lt;m:ctrlPr&gt;&lt;/m:ctrlPr&gt;&lt;/span&gt;&lt;/m:fPr&gt;&lt;m:num&gt;&lt;i     style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:     11.0pt;font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;km&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:num&gt;&lt;m:den&gt;&lt;i     style='mso-bidi-font-style:normal'&gt;&lt;sub&gt;&lt;span style='mso-bidi-font-size:     11.0pt;font-family:"Cambria Math","serif"'&gt;&lt;m:r&gt;s&lt;/m:r&gt;&lt;/span&gt;&lt;/sub&gt;&lt;/i&gt;&lt;/m:den&gt;&lt;/m:f&gt;&lt;/m:oMath&gt;&lt;/m:oMathPara&gt;&lt;![endif]--&gt;&lt;!--[if !msEquation]--&gt;&lt;span face="&amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;" style="font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"&gt;&lt;!--[if gte vml 1]&gt;&lt;v:shape  id="_x0000_i1025" type="#_x0000_t75" style='width:112.5pt;height:39pt'&gt; &lt;v:imagedata src="file:///C:\Users\mohit\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png"   o:title="" chromakey="white"/&gt;&lt;/v:shape&gt;&lt;![endif]--&gt;&lt;/span&gt;&lt;/p&gt;&lt;div class="separator" style="clear: both; text-align: center;"&gt;&lt;span face="&amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;" style="font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"&gt;&lt;a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6vOBfjGCjss8qLQFYTAdq4O8omATKWQQWE5hqIFjm5VdbfYQxvWXf1BPQNPacdMKOkl2FBDMNs09fTV9XYvVYWv0-0AEHLcB4MSNMAKJ0bPVKI_JQUU8R5nx2xSTMPaKmP5h5vu3FxQ/" style="margin-left: 1em; margin-right: 1em;"&gt;&lt;img alt="" data-original-height="170" data-original-width="526" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6vOBfjGCjss8qLQFYTAdq4O8omATKWQQWE5hqIFjm5VdbfYQxvWXf1BPQNPacdMKOkl2FBDMNs09fTV9XYvVYWv0-0AEHLcB4MSNMAKJ0bPVKI_JQUU8R5nx2xSTMPaKmP5h5vu3FxQ/w230-h74/image.png" width="230" /&gt;&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;&lt;span face="&amp;quot;Calibri&amp;quot;,&amp;quot;sans-serif&amp;quot;" style="font-size: 11pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: &amp;quot;Times New Roman&amp;quot;; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"&gt;&lt;br /&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-size: 11.0pt;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;p&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l1 level1 lfo1; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"&gt;&lt;span style="mso-list: Ignore;"&gt;3.&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;Polar Orbit [PO]&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l5 level1 lfo4; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Inclination of 90&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"&gt;°&lt;/span&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l5 level1 lfo4; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Used for &lt;b style="mso-bidi-font-weight: normal;"&gt;mapping &lt;/b&gt;or &lt;b style="mso-bidi-font-weight: normal;"&gt;surveillance &lt;/b&gt;operation.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l5 level1 lfo4; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Height higher than 250km.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l1 level1 lfo1; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"&gt;&lt;span style="mso-list: Ignore;"&gt;4.&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;Morniya Orbits&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l3 level1 lfo5; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Height eccentric earth orbits with T=12 hours.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l3 level1 lfo5; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Inclination are of 63.4&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"&gt;°&lt;/span&gt; &amp;amp; 116.6&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"&gt;°&lt;/span&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l3 level1 lfo5; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Provides good ground coverage at high northern latitudes.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l1 level1 lfo1; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"&gt;&lt;span style="mso-list: Ignore;"&gt;5.&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;Walking Orbits&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l6 level1 lfo6; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Subjected to several alternative gravitational force influences such like Sun, Moon and alternative planets.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l6 level1 lfo6; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Due to uneven forces, not excellent spherical form of planet &amp;amp; slightly uneven mass distribution leads to effect on spacecraft’s flight.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="mso-list: l1 level1 lfo1; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;span style="mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin;"&gt;&lt;span style="mso-list: Ignore;"&gt;6.&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;!--[endif]--&gt;&lt;b style="mso-bidi-font-weight: normal;"&gt;Sun Synchronous Orbit [SSO]&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpMiddle" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l2 level1 lfo7; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Same period as the planet’s solar orbit period are called Sun synchronous orbit.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt; &lt;p class="MsoListParagraphCxSpLast" style="margin-left: 0.75in; mso-add-space: auto; mso-list: l2 level1 lfo7; text-indent: -0.25in;"&gt;&lt;!--[if !supportLists]--&gt;&lt;span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"&gt;&lt;span style="mso-list: Ignore;"&gt;·&lt;span style="font: 7pt &amp;quot;Times New Roman&amp;quot;;"&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;Carry instruments which depend on a certain angle of solar illumination on the planet’s surface.&lt;b style="mso-bidi-font-weight: normal;"&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/b&gt;&lt;/p&gt;</description><link>https://aerogatetopper.blogspot.com/2021/05/types-of-orbits_5.html</link><author>noreply@blogger.com (Unknown)</author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" height="72" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhi69uKmddljfPudBbZu1DfWJljn0-THp0vEw0FA3VMLCFY46KT3FJY1TURPnNQdItGGqSuxfxqPS_3wc-urlxjQYWkHLvmUi9VbABRaH43JXzqwF-EP8glOU-K9fxhwU3TUf1jup3X9Q/s72-w219-h87-c/image.png" width="72"/><thr:total>0</thr:total></item></channel></rss>