List of top Questions asked in IIITH UGEE

Helium is two times heavier than H2. The average kinetic energy per molecule for helium at 300K is
When I was a child, there used to be a fair in my town during the Diwali and Id festivities. Among the many things I saw was a strange puppet show. There were three puppets, one of a man, another of a woman, and the third one of a rakshasa (demon). Whenever the rakshasa was brought close to the woman, she would turn her face away. But when the man was brought close to her, she would turn back and face the man.

Your teacher uses a weighing balance to take equal amounts of two substances, tartaric acid and washing soda, say 1g. Each is dissolved separately into 100 cc of water.

(A) In 1 drop of the acid solution and 1 drop of the basic solution, we have:
1. equal amount of acid and base respectively
2. equally acidic and basic substance respectively
3. acidity in one and basicity in the other are not equal
4. equal magnitude of the quantity —pH-7—
(B) Take a few cc of the acidic solution in a test-tube and mix a few drops of coloured
phenolphthaline solution (prepared in basic medium) into it. Which of the following may be 4
happening:
1. The colour of the solution instantly changes pink
2. remains colourless as the colour of the added drops disappears
3. the colour diffuses through the solution and finally disappears
4. the colour diffuses through the solution and finally the entire solution acquires a faint pink
colour.

How many solutions are there to the equation \(x_1 + x_2 + x_3 + x_4 = 17\), where \(x_1, x_2, x_3, x_4\) are nonnegative integers?

The function \( f(x) \) is defined as follows:  \[ f(x) = \begin{cases} 2+x, & \text{if } x \geq 0 \\ 2-x, & \text{if } x \leq 0 \end{cases} \] Then function \( f(x) \) at \( x=0 \) is: 

Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place?
A pair of fair dice is rolled. What is the probability that the second die lands on a higher value than the first?
Given below is an encrypted sentence: 
SJ HVJ HMM GPVC BHI. LPBJ VJBHEC LP. – LHBZJM GJFAJXX
Decode it based on the clues given below:
Clues:
  • Clue-1: H stands for A
  • Clue-2: B stands for E
  • Clue-3: C stands for N
  • Clue-4: L stands for S
  • Clue-5: I stands for D
A block of mass 2 kg is placed on a rough inclined plane at an angle of 30 degrees. The coefficient of friction between the block and the plane is 0.2. If the block is released from rest, will it slide down the plane? Justify your answer with calculations.
Explain the difference between work and energy. Give an example where work is done on an object, but its kinetic energy does not change.
A graph shows the velocity of an object as a function of time. Describe the motion of the object in detail, including its acceleration and displacement, at different points in time. What does the area under the curve represent?
Explain the difference between a strong acid and a weak acid. How does the pH of a solution change when a strong acid is added compared to a weak acid?
You are given 100 mL of a 0.1 M solution of HCl and 200 mL of a 0.2 M solution of NaOH. Calculate the pH of the resulting solution after mixing the two solutions.
You are given a set of experimental data for a chemical reaction, including the concentrations of reactants and products at different times. Determine the order of the reaction and the rate constant.
Explain the concept of a limit. Why is it important in calculus?
Find the equation of the tangent line to the curve \( y = x^2 - 3x + 2 \) at the point \( (1, 0) \).
You are given a sequence of numbers: 2, 5, 10, 17, ... Identify the pattern and find the next three terms in the sequence. Can you express the nth term of this sequence in a general formula?
Two chairs (A and B) are in an empty room overnight. Chair A is made of steel while chair B is made of wood. In the night and in the morning, the temperature of the room is 290 K. In the morning, a person chooses between Chair A and Chair B as the seat by feeling (touching) the chair and choosing one which feels warmer. 
Person chooses __ (BLANK-1) __ as it feels warmer because __ (BLANK-2)___ has __(BLANK-3)___ ___ (BLANK-4)____ than ___(BLANK-5)___ .
The velocity of the nitrogen molecule in room temperature air is:
Two liquids A and B are mixed in such a proportion that they form an ideal solution whose total vapor pressure is exactly three times that of the partial pressure of A. If \( P_A^\circ \) and \( P_B^\circ \) are the vapor pressures of pure A and B respectively, then the total vapor pressure of the solution is given by