IIITH UGEE 2024 Question Paper(Avaliable): Download Solution with Answer Key PDF

IIITH UGEE (SUPR) 2024 Question Paper with Solutions

Question 1:

Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, —–, 47

• (a) 34
• (b) 31
• (c) 38
• (d) 27
• (e) None of these

It is postulated that huge deposits of NaCl (rock salt) and CaCO3 (chalk and marble) are sites of erstwhile oceans, where the salts had been concentrated through weathering by rain and wind and leaching by rivers. Select the correct explanatory statement in this context.

• (a) Both NaCl and CaCO3 are highly soluble in water.
• (b) NaCl is soluble in water but CaCO3 is not. Hence, concentration of CaCO3 in the oceans through weathering is an untenable hypothesis.
• (c) The solubility of CaCO3 in water is pH dependent and is enhanced by acidic atmospheric gases. Hence, CaCO3 may be leached into water during weathering.
• (d) NaCl and CaCO3 are igneous rocks and have crystallized as such during the slow cooling process when the earth was born. Hence, the ocean postulates is baseless.

A known positive charge is located at point P as shown above, between two unknown charges, Q1 and Q2. P is closer to Q2 than Q1. If the net electric force acting on the charge at P is zero, it may correctly be concluded that:

• (A) Both Q1 and Q2 are positive
• (B) Both Q1 and Q2 are negative
• (C) Q1 and Q2 have opposite signs
• (D) Q1 and Q2 have the same sign, but magnitude of Q1 is greater than the magnitude of Q2

If log2 = 0.30103 and log3 = 0.4771, find the number of digits in (648)\(^5\).

• (a) 23
• (b) 15
• (c) 13
• (d) 14
• (e) 22

Which of the following solutions, when mixed, will not form a buffer solution?

• (a) 100 mL 0.1 M NaOH + 50 mL 0.1 M CH3COOH
• (b) 50 mL 0.1 M NaOH + 100 mL 0.1 M CH3COOH
• (c) 50 mL 0.1 M NH4OH + 50 mL 0.1 M CH3COOH
• (d) 50 mL 0.1 M HCl + 100 mL 0.1 M CH3COONa

A man can cover a distance in 1 hour 24 minutes by covering 2/3 of the distance at 4 km/h and the rest at 5 km/h. The total distance is

• (a) 2 km
• (b) 5 km
• (c) 6 km
• (d) 10 km
• (e) None of these

Three identical masses are at the three corners of the triangle, connected by massless identical springs (rest length \( l_0 \)) forming an isosceles right angle triangle. If the two sides of equal length (of length \( 2l_0 \)) lie along the positive x-axis and positive y-axis, then the force on the mass that is not at the origin but on the x-axis is given by \( \hat{i} + \hat{j} \) with \( a \) and \( b \).

• (a) \( a = 1 \) and \( b = 0 \)
• (b) \( a = 0 \) and \( b = 1 \)
• (c) \( a = -\sqrt{2} \) and \( b = 1 \)
• (d) \( a = -2 \) and \( b = 0 \)
• (e) \( a = -2 \) and \( b = 1 \)

Asim got thrice as many sums wrong as he got right. If he attempted 60 sums in all, how many sums did he solve correctly?

• (a) 25
• (b) 12
• (c) 20
• (d) 10
• (e) 15

A system consists of N particles, interacting with each other (for example, protein molecules). Which one of the following statements is FALSE?

• (a) The motion of the system can be split into translational, rotational, and vibrational motions
• (b) Number of rotational degrees of freedom are 3
• (c) Number of translational degrees of freedom are 3
• (d) Number of vibrational degrees of freedom are 3
• (e) The system, if isolated, will conserve both total energy and total angular momentum.

Three pipes A, B, and C can fill a tank in 6 hrs. After working at it together for 2 hrs, C is closed and A and B can fill the remaining part in 7 hrs. The total number of hours taken by C alone to fill the tank is

• (a) 14
• (b) 12
• (c) 11
• (d) 10
• (e) 13

A square closed loop of area A, lying in the horizontal plane, is moving horizontally with velocity \( v \) in a uniform vertical magnetic field \( B \). Which one of the following statements is FALSE?

• (a) There is current in the loop even though there is no battery (or any other voltage source)
• (b) The work done in moving the coil is being converted to the current in the coil
• (c) The current is being generated because the magnetic field is doing the work.
• (d) The emf generated is proportional to the velocity of the coil
• (e) The emf generated is proportional to the magnetic field strength

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

• (a) \( \frac{P_A^\circ P_B^\circ}{2} + P_A^\circ + P_B^\circ \)
• (b) \( 3P_A^\circ + P_B^\circ \)
• (c) \( \frac{P_A^\circ}{2} + P_B^\circ \)
• (d) \( P_A^\circ + 2P_B^\circ \)
• (e) More data needed to solve the problem

If \( P_0 \) and \( P_S \) are the vapour pressures of the solvent and solution respectively and \( X_0 \) and \( X_S \) are mole fractions of solvent and solute respectively, then

• (a) \( P_0 = X_S P_S \)
• (b) \( P_S = X_0 P_0 \)
• (c) \( P_0 = X_0 P_S \)
• (d) \( P_S = X_S P_0 \)

The velocity of the nitrogen molecule in room temperature air is:

• (a) zero
• (b) 10 m/s
• (c) 100 m/s
• (d) 500 m/s
• (e) 5000 m/s

Helium is two times heavier than H2. The average kinetic energy per molecule for helium at 300K is

• (a) twice as H2
• (b) same as H2
• (c) half as H2
• (d) one fourth of H2

IIITH UGEE (REAP) 2024 Question Paper with Solutions

Question 1:

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.

• (A) BLANK-1: Chair A, Chair B, neither chair
• (B) BLANK-2: metal, wood, air, human body
• (C) BLANK-3: higher, lower, different, same
• (D) BLANK-4: heat capacity, heat conductivity, electrical resistance
• (E) BLANK-5: metal, wood, air, human body

Consider a rope fixed at both ends under tension so that it is horizontal (i.e. assume the rope is along x-axis, with gravity acting along z-axis). Now the right end is continually oscillated at high frequency \( n \) (say \( n = 100 \, Hz \)) horizontally and in a direction along the rope; amplitude of oscillation is negligible. The oscillation travels along the rope and is reflected at the left end.

• (A) BLANK-1: travelling, oscillating, stationary, regular
• (B) BLANK-2: transverse, longitudinal, regular, irregular
• (C) BLANK-3: transverse, longitudinal, regular, irregular
• (D) BLANK-4: equal to, half, double, independent from
• (E) BLANK-5: \( \sqrt{\frac{g}{l}} \), \( \sqrt{m g} \), \( \sqrt{m g l} \), \( \sqrt{\frac{l}{g}} \)

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.


(A) The strange behaviour of the woman puppet was:

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|

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?

• (A) 1140
  (B) 1160
  (C) 1040
  (D) 1200
• (A) Continuous and differentiable.
• (B) Continuous but not differentiable.
• (C) Differentiable but not continuous.
• (D) Neither continuous nor differentiable.
• (A) \( ^{19}C_2 \)
• (B) \( ^{20}C_2 \)
• (C) \( ^{20}C_{19} \)
• (D) \( 20^2 \)
• (A) \( \frac{1}{36} \)
• (B) \( \frac{5}{36} \)
• (C) \( \frac{1}{6} \)
• (D) \( \frac{5}{12} \)
• (A) 1
• (B) 1.5
• (C) 2
• (D) 3