IIT JEE Blog

Conditional Probability

noreply@blogger.com (Manish Verma) — Sun, 26 Apr 2009 03:33:15 PDT

IIT JEE 2009 Paper-1 Physics Centre of Mass Problem

noreply@blogger.com (Manish Verma) — Sun, 19 Apr 2009 08:22:26 PDT

Prasanna - An IITM Alumnus

noreply@blogger.com (Manish Verma) — Sun, 22 Mar 2009 05:18:35 PDT

Refer: This article.

While this post may not be related to JEE directly, it may have inspirational value. Prasanna, an IIT Madras alumnus (senior to me) has done us proud. He is the composer of the original music of the Oscar award winning documentary, "Smile Pinky". I have seen him playing at OAT, CLT & SAC (IITM students/alumni must be familiar with these locations) and have sometimes taken inspiration from him to refine my guitar playing. While I am not a connoisseur of Carnatic music, it is my understanding that he has used his guitar playing skills in Carnatic music enormously. The string orchestra of the title track of the Oscar nominated movie, "Lagaan" composed by A. R. Rahman was arranged and conducted by Prasanna. He has also worked with Lakshmikant Pyarelal, Illayaraja*, Hariprasad Chaurasia, Sivamani** to name a few.

Changing his career stream after IITM degree, Prasanna pursued his passion for music and graduated from Berklee College of Music in Boston.

*Illayaraja is a well known film music composer. He has conducted show at IITM OAT during the annual function formerly called Mardi Gras (now called Saarang). In that show, S.P. Balasubrahmanyam & Chitra were also there.
**Sivamani is a well known drummer. He has performed at IITM OAT.

Q & A

noreply@blogger.com (Manish Verma) — Mon, 09 Feb 2009 23:11:37 PST

A non conducting ring of mass m and radius R has a charge Q uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that the plane of the ring is parallel to the surface. A vertical magnetic field B=B0t^2 Tesla is switched on. After t second from switching on the magnetic field the ring is just about to rotate about vertical axis through its centre. Find the friction coefficient between the ring and the surface.

Solution (.wmv download)

IIT JEE 2008, Paper I, Maths Section, Error

noreply@blogger.com (Manish Verma) — Thu, 28 Aug 2008 14:40:10 PDT

The detailed solution is provided in .pdf file which is taken from the source file of an eBooklet undergoing editing.

.pdf file

References:

IIT Website Answer
The Telegraph Article

Diffusion Vs Effusion

noreply@blogger.com (Manish Verma) — Wed, 13 Aug 2008 12:44:19 PDT

Diffusion: Imagine someone having perfume in her clothes entering a room and taking a seat close to the door while you are sitting on the opposite corner of the same room. Eventually, you are able to smell that perfume. This is due to the mixing of the perfume particles with air particles. However, it takes a while for you to be able to smell in spite of the fact that the molecules of the perfume travel very fast (hundreds of metres per second). This is due to the presence of other molecules of air in the room with whom perfume particles collide before reaching your nose. Effusion: Suppose, now we remove all other molecules - that is, we have vacuum - then, perfume particles are able to travel much faster. Effusion is the process of gas particles going through a hole into the vacuum and effusion takes place much more rapidly than diffusion since in effusion, collisions with external gas molecules are not involved.

Graham's law is more accurate for the effusion process and is approximately correct for the diffusion process as there are different gases involved in diffusion process.

Photograph of Shadow

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 11:55:43 PDT

Well, actually the question was a bit different. It was asked by an eager mind from class 9th. The question was, "It is said that black hole does not reflect light. But, I have seen the mention of picture of black hole in a magazine. How is this possible?"

The answer is hidden in the "picture" of the shadow that can be seen in the photograph. Actually, it is not the photograph of the shadow that is taken but the light is blocked from certain portion and that is called shadow. The photograph is taken for the remaining portion and the place where the light is blocked is shadow.

Q & A (Integral of Root Sin x)

noreply@blogger.com (Manish Verma) — Wed, 13 Aug 2008 12:49:51 PDT

Click Here

When the Doorbell Rings @ 4 AM......

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 11:57:35 PDT

8th July 2007

Initially, I thought to put this post this on another blog but later I thought that it had something to with Physics and decided to put it here.

At around 4 AM in the night amidst heavy rains if the doorbell rings then one can get suspicious at first. And if after checking one finds that there is no one at the door then it may be a feeling of relief with curiosity. I had this experience and since I was aware of such incident (doorbell ringing on its own), I was keen to investigate what could have caused this in my case. My doorbell was not wireless which could be triggered by the switch of my neighbour (if coincidentally both doorbells worked at same frequency). The bell I use is a musical bell connected to the switch via wires.

The bell under consideration plays music only once at the time of pressing the switch. If one continues to press the switch it won't keep on playing music. On the day the doorbell played music at 4 AM, it did not do so later even if someone pressed the switch. However, when the mains power was switched off and switched on again, the doorbell did play music. Now, it looked as if at 4 AM something caused the two wires in the switch to come in electrical contact. When it happened first (i.e. at 4 AM on that day), there was music. Subsequently, since the wires remained in electrical contact, pressing the switch was irrelevant and doing so did not cause it to play music. When the mains was switched off, now even though those two wires remained in electrical contact, there was disconnection in the circuit and it played music when the mains was switched on.

While all these experiments confirm the theory that at 4 AM on that particular day, the two wires did come into contact, one can still wonder what could have caused them to come in contact. Was it wind? But then inside the switch where two wires are there, the effect of wind should be subdued. Since switch is outside, it could be the rain causing the two points to come in electrical contact (it doesn't necessarily have to be a physical contact). The water can find its way through a switch which is not water tight.

5th May 2008

I have been thinking about updating this post since a past few months. The bell rang later after rainy season when there were no rains. I tried to see inside the switch to investigate what could be responsible for the electrical contact and I could find a wasp there.

IIT JEE 2008 Paper I Maths Calculus Write Up

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 11:59:05 PDT

.pdf file

Sound Waves

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 11:59:50 PDT

Here are some additional points which may be useful besides the standard discussion of Doppler's Effect.

If listener is moving towards the source (irrespective of source moving towards, away or remaining stationary) then the listener is able to get the waves more quickly. In this case the speed of sound for the listener is more. For example in a write-up based question in JEE 2007*, the engine of train A was blowing whistle and the speed of sound for the passenger of the same train would be 340+20=360 m/s.
If listener is moving away from the source (irrespective of the source moving towards, away or remaining stationary) then the listener is able to get the waves with some delay (it is as if the listener is running away from them). In this case the speed of sound for the listener is less. For example in a write-up based question in JEE 2007*, the engine of train A was blowing whistle and the speed of sound for the passenger of train B moving in front would be 340-30=310 m/s.
When source is moving towards or away from the listener (irrespective of the motion of the listener) then the wavelength changes. If source is not moving wavelength does not change. This is because if the source is moving (say) towards the listener, then the distance between the two consecutive wavefronts would be smaller (second wavefront leaves the source when it already have moved forward). If the source is moving away from the listener, then the distance between the two consecutive wavefronts would be more (second wavefront leaves the source when the source has moved backward).

*Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle. The speed of sound in still air is 340 m/s.

Atomic Structure

noreply@blogger.com (Manish Verma) — Sat, 29 Mar 2008 01:23:17 PDT

A spectroscopic instrument can resolve two nearby wavelengths and if is smaller than 8,000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument?

Vector

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 12:01:03 PDT

A carrom board (4ft x 4ft) has the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen from (a) from the centre of the front edge, (b) from the front edge to the hole and (c) from the centre to the hole.

The solution is embedded as part of live recording done during a class.

Rolling Friction

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 12:01:48 PDT

Rolling friction is due to the deformation taking place at the surface of a rolling ball. It is responsible to decrease the velocity of the centre of mass of the rolling ball and hence plays a part in stopping the ball.

Self-Orthogonal Visualisation

noreply@blogger.com (Manish Verma) — Tue, 09 Dec 2008 03:39:21 PST

A family of ellipse whose one member is shown in the figure is not expected to be self-orthogonal. But, when the equation

is analysed using differential equation technique, one finds that the equation does represent self-orthogonal trajectory. How does one visualise this type of trajectory?

The answer lies in the possible values of which is a parameter or arbitrary constant. The expression can become negative for several negative values of and hence the curve can become hyperbola. Now, one can visualise self-orthogonality in the following manner:
It can be seen that the curves above intersect at 90 degrees.

Pen Mouse / Pen Tablet

noreply@blogger.com (Manish Verma) — Tue, 09 Dec 2008 03:39:21 PST

Virtual classroom can be a greater place of collaboration when students are given "write" access to the whiteboard. By enabling, "write" access to the whiteboard, it is found that generally students are very careful about what they write there (the awareness that class is being recorded might have added to this carefulness). Since virtual classroom whiteboard already has built-in ways to draw/type circles, ellipses, lines, rectangles, co-ordinate axes, text etc., one can manage to draw/type with mouse with occasional need to use free-hand feature. However, those students who want to go a step further with free-hand usage can try pen mouse / pen tablet which is a simple device that can be connected to the PC via USB. Availability of brands may depend on the place, but in India, "iBall" is worth mentioning and, "Wacom" should be available in many places globally. Some models also have wireless mouse besides pen but it is not required as the earlier mouse continues to work. The pen itself can be a partial replacement of conventional mouse after getting accustomed to it.

Online IIT-JEE Test (OETS/OTS) Via Mobile

noreply@blogger.com (Manish Verma) — Sun, 31 May 2009 11:48:18 PDT

Objective test does not require typing a lot and if it can work in mobile just fine then it can have a great utility especially when electrical power reliability is an issue. Mobile phone handset and service provider of course must support this.

Here is the screenshot of a part of the test I performed using N73 at courses management system at 123iitjee.net in a part of OETS 08. The timer works fine (N73 browser supports javascript), there was no problem with cookies (cookies must be enabled for login and there is no problem with that). Images display properly and equations look great. Options can be chosen (text size adjustment helps which is provided in the browser of the handset) for different types of questions (like JEE 2006/2007 types) and finally questions are graded just fine along with the answers given with feedback etc. after the test is submitted. The review of the test shows everything the way it should be. Those students having access to mobile internet can give it a try.

Google Sky

noreply@blogger.com (Manish Verma) — Sun, 26 Aug 2007 05:23:48 PDT

Indians - Believe in Yourself

noreply@blogger.com (Manish Verma) — Tue, 09 Dec 2008 03:39:21 PST

As India continues to rise, the belief in Indians that they are nothing less is important. The dominance of the western world, western names in science and other fields may make a non-westerner start doubting his/her own abilities.

Any student of science/maths gets to hear about more and more western names given the credit for inventions/discoveries. Many voices have been raised by different people in India to claim otherwise on several fronts. But, these voices have not risen to enhance each other collectively but have been raised singularly.

Students of science/maths at 10+ level know about the importance of calculus. One can not imagine about learning Physics without being exposed to calculus. When one learns chapter on gravitation, one can occasionally read that calculus was invented by Newton and Leibniz. One can find the mention of the same names while learning calculus. The following is mentioned in page 319, new NCERT maths eBook for class 11th:

Here is a good news to cherish and to make us believe in our abilities:

Calculus Created in India 250 Years Before Newton: Study

The progress of a civilisation largely depends on the dreams of the people. Dreams are influenced by role models. It is important that the hidden real heroes are brought into the limelight. I hope that revelations like this invoke self-belief, inspire dreams leading towards achievement and contribution.

Determination Of Alcohol Content In Blood

noreply@blogger.com (Manish Verma) — Wed, 01 Aug 2007 00:09:20 PDT

Because blood passes through the arteries in the lungs, an equilibrium is established between the alcohol in one's blood and the alcohol in one's breath. So if the concentration of one is known, the concentration of the other can be estimated.

The test that law enforcement agencies use to approximate a person's blood alcohol level is based on the oxidation of breath ethanol by sodium dichromate. A sealed glass tube is used, which contains the oxidising agent impregnated onto an inert material. The ends of the tube are broken off. One end of the tube is attached to a mouthpiece and the other to a balloon-type bag. The person undergoing the test blows into the mouthpiece until the bag is filled with air.

Ethanol in the breath is oxidized as it passes through the column. When ethanol is oxidized, the red-orange oxidizing agent (Cr₂O₇^2-) is reduced to green chromic ion. The greater the concentration of alcohol in the breath, the farther the green colour spreads through the tube.

C₂H₅OH + Cr₂O₇^2----------> Cr⁺³+ CH₃COOH
red-orange green

If the person fails this test — determined by the extent to which the green colour spreads through the tube — a more accurate Breathalyser test is administered. This test also depends on the oxidation of breath ethanol by sodium dichromate, but it provides more accurate results. Here, an accurate volume of breath is bubbled through an acidic solution of sodium dichromate. The concentration of chromic ion is measured precisely using a spectrophotometer.

Contributed by: Mr Devender Singh, dev_chem2002@yahoo.co.in .

Kekule's Dream

noreply@blogger.com (Manish Verma) — Fri, 27 Jul 2007 23:51:14 PDT

Friedrich August Kekule von Stradonitz (1829-1896) was born in Germany. He entered the University of Giessen to study architecture but switched to chemistry after taking a chemistry course. He was a professor of chemistry at the University of Heidelberg, at the University of Ghent in Belgium, and then at the University of Bonn. In 1890, he gave an extemporaneous speech at the twenty-fifth anniversary celebration of his first paper on the cyclic structure of benzene. In this speech he claimed that he had arrived at the Kekule structure as a result of dozing off in front of a fire while working on a textbook. He dreamed of chains of carbon atoms twisting and turning in a snakelike motion, when suddenly the head of one snake seized hold of its own tail and formed a spinning ring. Recently, the veracity of his snake story has been questioned by those who point out that there is no written record of the dream from the time he experienced it in 1861 until the time he related it in 1890. Others counter that dreams are not the kind of evidence one publishes in scientific papers. But it is not uncommon for scientists to report moments of creativity through the unconscious, when they were not thinking about science. After relating his dream, Kekule said, "Let us learn to dream, and perhaps then we shall learn the truth. But let us also beware not to publish our dreams until they have been examined by the wakened mind." In 1895, he was made a nobleman by Emperor William II. This allowed him to add "von Stradonitz" to his name. Kekule's students received three of the first five Nobel Prizes in chemistry: van't Hoff in 1901, Fischer in 1902, and Baeyer in 1905.

Contributed by Mr S. Devender Singh, dev_chem2002@yahoo.co.in .

Subjective Vs Objective

noreply@blogger.com (Manish Verma) — Mon, 18 Aug 2008 12:04:08 PDT

If IIT JEE is objective exam then should one prepare doing subjective questions?

According to the new pattern IIT JEE, there is lot of emphasis on, "comprehension" and "analytical ability". Comprehension simply means understanding things at deep level and it does not just imply linked comprehension type of questions. Analytical ability means application of what has been comprehended in different/new situations. Essentially this is what IIT JEE has been over many years. The objective paper is a good friend of teachers who are made to evaluate lakhs of subjective answer copies. One can easily see that Olympiads toppers continue to do well in IIT JEE. Olympiads are subjective type of exams which test deep understanding ability and problem solving approach with greater difficulty level than that of IIT JEE. Objective questions in IIT JEE are like subjective questions in new bottle. However, keeping in view the fact that a student must be prepared to handle new situations in addition to comprehension, a student should do subjective problems and innovative objective problems. At the end of the day, it is his/her understanding and application that are going to sail him/her through.

NCERT - Log misses the bus!

noreply@blogger.com (Manish Verma) — Sun, 15 Jul 2007 00:33:01 PDT

While Log tables as tools for calculation may be facing their extinction due to the "fitter" electronic calculators, Log continues to be important as it seems be an ingredient of some laws of nature. Effort to find Log as a chapter in NCERT syllabi (9th, 10th, 11th & 12th) would go in vain. If one tries hard enough then one finds the mention of Logarithmic series in the appendix of class 11th Mathematics. One wonders if there in no Log in class 11th or earlier then how can there be Logarithmic series in appendix? After all shouldn't Log be taught first? A search of word Log does not show anywhere else in class 11th portion. But then shouldn't Log be there in class 11th (or earlier)? After all there are so many applications in quadratic expressions & equations that are based on Log, so many problems related to domain & range based on Log, concept of pH, Henderson's equation for buffer solutions, work done in an isothermal process by an ideal gas etc. All the topics mentioned above are in class 11th portion. Finally, one can find Log in class 12th syllabus inside, "Continuity & Differentiability" which is after, "Functions". To get a feel of functions, it is necessary that students get into graphing but if NCERT is to be followed then graphs of Log cannot be understood properly when graphs of most standard and special functions are discussed. A simple and widely used topic Log must be introduced in early class formally and not so late. In fact in the past it was introduced before class 11th and it makes sense as students are introduced to pH before class 11th level.

NCERT should include Log in earlier class in future but at the moment, teachers should consider it including in 11th portion if not earlier.

Dr. H. C. Verma's Interview

noreply@blogger.com (Manish Verma) — Sun, 15 Jul 2007 09:01:09 PDT

Here is around 30 min. of the interview:

Q & A: Potential Inside Dielectric Sphere

noreply@blogger.com (Manish Verma) — Sat, 06 Oct 2007 12:54:17 PDT

This is in reply to a question asked in the class. Hope it is helpful to others as well.