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IIT JEE Mains/JEE Advanced @LWS - Learn With Saras

2025-02-11T17:49:00.002+05:30

Chemistry from Aayushi Ma'm (Former Chemistry Faculty at Aakash, AskIITian)

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Math and Physics from Saras Ojha (B.Tech NIT Jaipur, M.Tech IIT (BHU))

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🔹 Subjects Offered:

Mathematics
Physics

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✔️ Experienced Teacher with a proven track record of success in IIT JEE coaching.
✔️ In-depth Conceptual Clarity — Building a strong foundation for both subjects.
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Batch and One-on-One Classes available.

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Some Interesting Excerpts from the book, "Brighter than the Thousand Suns"

2025-02-07T17:40:00.011+05:30

Oppenheimer taught not only at Berkeley but also at the California Institute of Technology in Pasadena. As soon as he ended a course of lectures at the university most of his students would follow him, for the ensuing term, to this second seat of learning near Los Angeles. Despite his youth, 'Oppie', as they called him, had come to be looked upon as a master and model by the rising generation of physicists in America, just as the great men of atomic research in Europe had been regarded by himself only a few years before. The veneration felt by the students for their hero was so great that consciously or unconsciously they imitated many of his personal peculiarities. They held their heads a little on one side just as he did. They coughed Slightly and paused significantly between successive sentences. They held their hands in front of their lips when they spoke. Their ways of expressing themselves were often difficult to understand. They were fond of making obscure comparisons which Sounded most pregnant and sometimes actually were so. Oppenheimer, himself a confirmed smoker, had the habit of clicking open his lighter and jumping up whenever anyone took out a cigarette or pipe. His students could be recognized from afar in the campus cafeterias Of Berkeley and Pasadena by their custom of darting about from time to time, like marionettes on invisible strings, with tiny flames between their fingers.

'Many physicists only have high-voltage current in their veins,' said someone who had known him a long time. ‘But Sam has blood. He knows that the world contains other interesting things besides equations and cyclotrons.' It was typical of Goudsmit that he gave the following advice to a young nuclear physicist who wanted to go to an atom-bomb test in Nevada. 'If you want to see a show, why don't you buy a ticket to one of the current Broadway musicals? That might help you more with your work than going west. Pauli won the Nobel prize by going to the theatre, you know. He was watching a revue in Copenhagen when the exclusion principle came to him.'

III

As early as the spring of 1945 a study group within the Manhattan Project was given the task of selecting a target for the first employment of the bomb. The group comprised mathematicians, theoretical physicists, specialists on the effects of explosions and meteorological experts. This team, mainly composed of scientists, including Robert Oppenheimer, came to the conclusion, according to a report published later in a limited edition by the Manhattan Engineer District, that targets for this peculiar type of bomb must satisfy the following conditions: (a) Since the atomic bomb is expected to produce its greatest amount of damage by primary blast effect and next greatest by fires, the targets should contain a large percentage of closely built frame buildings and other construction that would be most susceptible to damage by blast and fire; (b) the maximum blast effect of the bomb is calculated to extend over an area of approximately one mile in radius. Therefore the selected targets should contain a densely built-up area of at least this size; (c) the targets selected should possess high military and strategic value; (d) the first target should if possible be one that has escaped earlier bombardments, so that the effect of a single atomic bomb can be ascertained. It was further resolved that four Japanese cities should be deliberately spared bombardment by the American formations which by 1945 could reconnoitre any target they pleased in Japan with practically no resistance. This deceptive period of grace was granted these four cities so they could be doomed to a ruin all the more dreadful by the new bomb.

On 21 May 1946, not quite a year later, Slotin was carrying out an experiment, similar to those he had so often successfully performed in the past. It was connected with the preparation of the second atom-bomb test, to be performed in the waters of the South Sea atoll of Bikini. Suddenly his screwdriver slipped. The hemispheres came too close together and the material became critical. The whole room was instantly filled with a dazzling, bluish glare. Slotin, instead of ducking and thereby possibly saving himself, tore the two hemispheres apart with his hands and thus interrupted the chain reaction. By this action he saved the lives of the seven other persons in the room. He had realized at once that he himself would be bound to succumb to the effects of the excessive radiation dose which he had absorbed. But he did not lose his self-control for a moment. He told his colleagues to go and stand exactly where they had been at the instant of the disaster. He then drew on the blackboard, with his own hand, an accurate sketch of their relative positions, so that the doctors could ascertain the degree of radiation to which each of those present had been exposed.

Strange to say, a terrible fate was also in store for the complement of the cruiser Indianapolis, which took to Tinian the greater part of the explosive heart of the first atom bomb destined for use against Japan. Only three men aboard the vesse2 the fastest in the American fleet, had any idea what she was carrying. The rest simply supposed that there must be something very important in the big wooden case which had been hoisted aboard, with every precaution, on the morning of 16 July shortly before the ship put to sea. During the voyage from San Francisco to Tinian very special security measures were taken for defence against hostile submarines. Everyone heaved a sigh of relief when the Indianapolis, after unloading her secret cargo at Tinian, stood for the offing. But before the cruiser had reached her second port of call she was struck, at five minutes past midnight on 30 July, by a torpedo. Owing to a series of unfortunate circumstances news of the sinking did not reach naval headquarters for another four days. Signals from another ship were wrongly taken to be routine reports from the Indianapolis of her position and owing to one more misunderstanding she was not reported as overdue at Leyte harbour. Therefore, salvage units arrived too late at the scene of the disaster, and of the ship's 1,196 men only 316 were rescued. Some days before the first test of the bomb it was an open secret in Alamogordo, even among the wives and children of the Los Alamos scientists, that some particularly important and exciting event was in preparation. The test was referred to under the code name 'Trinity'. No clear explanation has hitherto been forthcoming as to why this blasphemous expression was employed, above all in such a connexion. One probability is that it was taken from the name of a turquoise mine near Los Alamos, which had been laid under a curse and therefore abandoned by the superstitious Indians. Another guess supposes that it was chosen because at that time the first three atom bombs were approaching completion, and that the code name was derived simply and solely from the existence of that hellish trinity.

During the ensuing period of waiting, which seemed an eternity, hardly a word was spoken. Everyone was giving free play to his thoughts. But so far as those who have been asked can remember, these thoughts were not apocalyptic. Most of the people concerned, it appears, were trying to work out how long it would be before they could shift their uncomfortable position and obtain some kind of view of the spectacle awaited. Fermi, experimental- minded as ever, was holding scraps of paper, with which he meant to gauge the air pressure and thereby estimate the strength of the explosion the moment it occurred. Frisch was intent on memorizing the phenomenon as precisely as possible, without allowing either excitement or preconceived notions to interfere with his faculties of perception. Groves was wondering for the hundredth time whether he had taken every possible step to ensure rapid evacuation in the case of a disaster. Oppenheimer oscillated between fears that the experiment would fail and fears that it would succeed.

VII

Even so cool and matter-of-fact a person as Enrico Fermi received a profound shock, in spite of the retort he had made to all the objections of his colleagues to the bomb during the discussions of the past few weeks. He had always said: 'Don't bother me with your conscientious scruples! After all, the thing's superb physics!' Never before had he allowed anyone else to drive his car. But on this occasion he confessed that he did not feel capable of sitting at the wheel and asked a friend to take it for him on the road back to Los Alamos. He told his wife, the morning after his return, that it had seemed to him as if the car were jumping from curve to curve, skipping the straight stretches in between.

VIII

Nishina started next day, for the second time, on his flight to Hiroshima, still hoping that he might after all have been mistaken. In addition to the sorrow he felt as a patriot he was also tormented by the fear that if a scientific superweapon of this kind had really been constructed and used, the scientists of the West, his friends over so many years, in the eyes of the Japanese people would now be inhuman monsters. When on the afternoon of 8 August his aircraft came within sight of the huge, smoking heap of ruins that had once been a flourishing city, all his fears were confirmed. Later he told the American officers who cross examined him: 'As I surveyed the damage from the air, I decided at a glance that nothing but an atomic bomb could have created such devastation.

Worksheets

2023-10-29T15:03:00.003+05:30

We have created some free worksheets for students of IB (MYP 4 and MYP 5), IB AA HL, Cambridge IGCSE, and AS and A Level students.

Worksheets are documented topic wise and can be accessed via left hand navigation.

You can post your answers in the comment section and I will respond to it.

Thank you.

Leet Code Java Solution - Container with Most Water

2021-10-21T23:27:00.004+05:30

Given n non-negative integers a1, a2, ..., an , where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of the line i is at (i, ai) and (i, 0). Find two lines, which, together with the x-axis forms a container, such that the container contains the most water.

Notice that you may not slant the container.

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.

Example 2:

Input: height = [1,1]
Output: 1

Example 3:

Input: height = [4,3,2,1,4]
Output: 16

Example 4:

Input: height = [1,2,1]
Output: 2

Constraints:

n == height.length
2 <= n <= 105
0 <= height[i] <= 104

My Code:

class Solution {

public int maxArea(int[] height) {

int maxWater = 0;

int left = 0;

int right=height.length -1;

while (left<right){

maxWater = Math.max(maxWater, (right-left)*Math.min(height[left],height[right]));

if (height[left]<height[right]) left ++;

else right --;

}

return maxWater;

}

Alternate Code:

class Solution {

public int maxArea(int[] height) {

int [] [] area = new int[height.length][height.length];

int prod = 0;

for (int i = 0; i<height.length;i++){

for(int j=i+1;j< height.length;j++){

int distance = Math.abs(j-i);

if (height[i]<height[j]){

area[i][j-1] = height[i]*distance;

}

else{

area[i][j-1] = height[j]*distance;

}

for (int i = 0; i<height.length;i++){

for (int j =0; j<height.length;j++){

if (area[i][j]>prod){

prod = area[i][j];

}

return prod;

}

Reversing a String - Practice

2021-10-21T13:53:00.002+05:30

Problem: The output should be reverse of a string input.

For example, Input: greatlearning;

Output: gninraeltaerg;

Input: to;

Output: ot;

public class reversingString {

public static void main(String[] args) {

// TODO Auto-generated method stub

String original = "greatlearning";

reversingString obj = new reversingString();

char [] get_result = obj.mirrorstring(original);

System.out.println(get_result);

}

public char[] mirrorstring(String original){

char [] chars = original.toCharArray();

for (int i=0,j=0; i<chars.length && j<chars.length/2; i++,j++){

char ch = chars[chars.length-1-j];

chars[chars.length-1-j] = chars[i];

chars[i]= ch;

}

return chars;

}

Leet Code Java Solution - Verifing an Alien Dictionary

2021-10-21T12:05:00.007+05:30

In an alien language, surprisingly, they also use English lowercase letters, but possibly in a different order. The order of the alphabet is some permutation of lowercase letters.

Given a sequence of words written in the alien language, and the order of the alphabet, return true if and only if the given words are sorted lexicographically in this alien language.

Example 1:

Input: words = ["hello","leetcode"], order = "hlabcdefgijkmnopqrstuvwxyz"
Output: true
Explanation: As 'h' comes before 'l' in this language, then the sequence is sorted.

Example 2:

Input: words = ["word","world","row"], order = "worldabcefghijkmnpqstuvxyz"
Output: false
Explanation: As 'd' comes after 'l' in this language, then words[0] > words[1], hence the sequence is unsorted.

Example 3:

Input: words = ["apple","app"], order = "abcdefghijklmnopqrstuvwxyz"
Output: false
Explanation: The first three characters "app" match, and the second string is shorter (in size.) According to lexicographical rules "apple" > "app", because 'l' > '∅', where '∅' is defined as the blank character which is less than any other character (More info).

Constraints:

1 <= words.length <= 100
1 <= words[i].length <= 20
order.length == 26
All characters in words[i] and order are English lowercase letters.

My Code:

class Solution {

public boolean isAlienSorted(String[] words, String order) {

for(int i=0;i<words.length-1;i++)

{

boolean allEqual= false;

for(int j=0;j<words[i].length() && j<words[i+1].length();j++){

if(order.indexOf(words[i].charAt(j))<order.indexOf(words[i+1].charAt(j))){

allEqual = true;

break;

}

else if(order.indexOf(words[i].charAt(j))>order.indexOf(words[i+1].charAt(j))){

return false;

}

if (!allEqual && words[i+1].length()< words[i].length()){

return false;

}

return true;

}

Leet Code Java Solution - Valid Anagram

2021-10-21T11:21:00.002+05:30

Given two strings s and t, return true if t is an anagram of s, and false otherwise.

Example 1:

Input: s = "anagram", t = "nagaram"
Output: true

Example 2:

Input: s = "rat", t = "car"
Output: false

Constraints:

1 <= s.length, t.length <= 5 * 104
s and t consist of lowercase English letters.

My Code:

class Solution {

public boolean isAnagram(String s, String t) {

char c1[] = s.toCharArray();

char c2[] = t.toCharArray();

Arrays.sort(c1);

Arrays.sort(c2);

if(Arrays.equals(c1, c2)){

return true;

}

else{

return false;

}

Leet Code Java Solution - First Bad Version

2021-10-21T11:18:00.005+05:30

You are a product manager and currently leading a team to develop a new product. Unfortunately, the latest version of your product fails the quality check. Since each version is developed based on the previous version, all the versions after a bad version are also bad.

Suppose you have n versions [1, 2, ..., n] and you want to find out the first bad one, which causes all the following ones to be bad.

You are given an API bool isBadVersion(version) which returns whether version is bad. Implement a function to find the first bad version. You should minimize the number of calls to the API.

Example 1:

Input: n = 5, bad = 4
Output: 4
Explanation:
call isBadVersion(3) -> false
call isBadVersion(5) -> true
call isBadVersion(4) -> true
Then 4 is the first bad version.

Example 2:

Input: n = 1, bad = 1
Output: 1

Constraints:

1 <= bad <= n <= 231 - 1

My Code:

/* The isBadVersion API is defined in the parent class VersionControl.

boolean isBadVersion(int version); */

public class Solution extends VersionControl {

public int firstBadVersion(int n) {

int i=0, j =n, mid=0;

while(i<=j){

mid = i + (j-i) / 2;

if(!isBadVersion(mid)) i = mid+1;

else j = mid-1;

}

if(!isBadVersion(mid)) return mid+1;

return mid;

}

Leet Code Solution JAVA - Guess Number Higher or Lower

2021-10-21T11:13:00.001+05:30

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I will tell you whether the number I picked is higher or lower than your guess.

You call a pre-defined API int guess(int num), which returns 3 possible results:

-1: The number I picked is lower than your guess (i.e. pick < num).
1: The number I picked is higher than your guess (i.e. pick > num).
0: The number I picked is equal to your guess (i.e. pick == num).

Return the number that I picked.

Example 1:

Input: n = 10, pick = 6
Output: 6

Example 2:

Input: n = 1, pick = 1
Output: 1

Example 3:

Input: n = 2, pick = 1
Output: 1

Example 4:

Input: n = 2, pick = 2
Output: 2

Constraints:

1 <= n <= 231 - 1
1 <= pick <= n

My Code:

/**

* Forward declaration of guess API.

* @param num your guess

* @return -1 if num is lower than the guess number

* 1 if num is higher than the guess number

* otherwise return 0

* int guess(int num);

public class Solution extends GuessGame {

public int guessNumber(int num) {

int i=1, j=num, mid=1;

while(i<=j){

mid = i + (j-i) / 2;

int result = guess(mid);

if(result==1) i = mid+1;

else if (result==-1) j = mid-1;

else return mid;

}

return mid;

}

Leet Code JAVA Solution - Angle Between Hands of a Clock

2021-10-21T11:01:00.002+05:30

Given two numbers, hour and minutes. Return the smaller angle (in degrees) formed between the hour and the minute hand.

Example 1:

Input: hour = 12, minutes = 30
Output: 165

Example 2:

Input: hour = 3, minutes = 30
Output: 75

Example 3:

Input: hour = 3, minutes = 15
Output: 7.5

Example 4:

Input: hour = 4, minutes = 50
Output: 155

Example 5:

Input: hour = 12, minutes = 0
Output: 0

Constraints:

1 <= hour <= 12
0 <= minutes <= 59
Answers within 10^-5 of the actual value will be accepted as correct.

My Code:

class Solution {

public double angleClock(int hour, int minutes) {

double angle = 5.5*(minutes + (hour)*60);

if (angle < 360 && angle > 180){

return (360 -angle);

}

else if (angle>360){

double n = angle%360;

if(n>180){

return (360 - n);

}

else{

return n;

}

else if(angle<0){

return (-angle);

}

return 0;

}

Leet Code Solution Java - Two Sum

2021-10-18T22:20:00.001+05:30

Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target.

You may assume that each input would have exactly one solution, and you may not use the same element twice.

You can return the answer in any order.

Example 1:

Input: nums = [2,7,11,15], target = 9
Output: [0,1]
Output: Because nums[0] + nums[1] == 9, we return [0, 1].

Example 2:

Input: nums = [3,2,4], target = 6
Output: [1,2]

Example 3:

Input: nums = [3,3], target = 6

Output: [0,1]

Code:

class Solution {

public int[] twoSum(int[] nums, int target) {

int [] arr = new int [2];

for (int i=0; i<nums.length;i++){

for(int j=i+1;j<nums.length; j++){

int add = nums[i]+nums[j];

if(add==target){

arr[0] = i;

arr[1] = j;

}

return arr;

}