Part-III : Physics
Section- I (Single Correct Choice Type)
This Section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.
1. Consider a thin square sheet of side L and thickness t, made of a material of resistivity p. The resistance between two opposite faces, shown by the shaded areas in the figure is
(A) directly proportional to L
(B) directly proportional to t
(C) independent of L
(D) independent of t
2. A real gas behaves like an ideal gas if its
(A) pressure and temperature are both high
(B) pressure and temperature are both low
(C) pressure is high and temperature is low
(D) pressure is low and temperature is high
3. Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R100, R60 and R40, respectively, the relation between these resistances is
(A) 
(B) 
(C) 
(D) 
4. To Verify Ohm’s law, a student is provided with a test resistor RT, a high resistance R1, a small resistance R2, two identical galvanometers G1 and G2, and a variable voltage source V. The correct circuit to carry out the experiment is
(A) 
(B) 
(C) 
(D) 
5. An AC voltage source of variable angular frequency ω and fixed amplitude V0 is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased
(A) the bulb glows dimmer
(B) the bulb glows brighter
(C) total impedance of the circuit is unchanged
(D) total impedance of the circuit increases
6. A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is
(A) 
(B) 
(C) 
(D) 
7. A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P1 = mg(sin θ − μ cos θ) to P2 = mg(sin θ + μ cos θ), the frictional force f versus P graph will look like
(A) 
(B) 
(C) 
(D) 
8. A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
(A) 
(B) 
(C) 
(D) 
SECTION – II (Multiple Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONE OR MORE may be correct.
9. A few electric field lines for a system of two charges Q1 and Q2 fixed at two different points on the x-axis are shown in the figure. These lines suggest that
(A) |Q1| > |Q2|
(B) |Q1| < |Q2|
(C) at a finite distance to the left of Q1 the electric field is zero
(D) at a finite distance to the right of Q2 the electric field is zero
10. A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?
(A) Error ΔT in measuring T, the time period, is 0.05 seconds
(B) Error ΔT in measuring T, the time period, is 1 second
(C) Percentage error in the determination of g is 5%
(D) Percentage error in the determination of g is 2.5%
11. A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms−1. Which of the following statement(s) is (are) correct for the system of these two masses?
(A) Total momentum of the system is 3 kg ms−1
(B) Momentum of 5 kg mass after collision is 4 kg ms−1
(C) Kinetic energy of the centre of mass is 0.75 J
(D) Total kinetic energy of the system is 4J
12. A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure). If the refractive index of the material of the prism is √3 , which of the following is (are) correct?
(A) The ray gets totally internally reflected at face CD
(B) The ray comes out through face AD
(C) The angle between the incident ray and the emergent ray is 90°
(D) The angle between the incident ray and the emergent ray is 120°
13. One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P0. Choose the correct option(s) from the following
(A) Internal energies at A and B are the same
(B) Work done by the gas in process AB is P0V0 ℓn 4
(C) Pressure at C is P0/4
(D) Temperature at C is T0/4
SECTION –III (Paragraph Type)
This section contains 2 paragraphs. Based upon the first paragraph 2 multiple choice questions and based upon the second paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices A), B), C) and D) out of WHICH ONLY ONE CORRECT.
Paragraph for Questions 14 to 16
When a particle of mass m moves on the x-axis in a potential
of the form V(x) = kx2 it performs simple harmonic motion. The corresponding time period is proportional to 
as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different
from kx2 and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx4 (α > 0) for |x| near the origin and becomes a constant equal to V0 for |x| ≥ X0 (see figure).
14. If the total energy of the particle is E, it will perform periodic motion only if
(A) E < 0
(B) E > 0
(C) V0 > E > 0
(D) E > V0
15. For periodic motion of small amplitude A, the time period T of this particle is proportional to
(A) 
(B) 
(C) 
(D) 
16. The acceleration of this particle for |x| > X0 is
(A) proportional to V0
(B) 
(C) 
(D) zero
Paragraph for Questions 17 to 18
Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc(0) if they are placed in a magnetic field, i.e., the critical temperature Tc (B) is a function of the magnetic field strength B. The dependence of Tc(B) on B is shown in the figure.
17. In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B2 (dashed line). If B2 is larger than B1 which of the following graphs shows the correct variation of R with T in these fields?
(A) 
(B) 
(C) 
(D) 
18. A superconductor has TC (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when
(A) B = 5 Tesla, Tc (B) = 80 K
(B) B = 5 Tesla, 75 K < Tc (B) < 100 K
(C) B = 10 Tesla, 75K < Tc < 100 K
(D) B = 10 Tesla, Tc = 70K
SECTION –IV (Integer Type)
This section contains TEN questions. The answer to each question is a single digit integer ranging from 0 to 9.
19. The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m25 to m50. The ratio 
is
20. An α- particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are λα and λp The ratio λp/ λα, to the nearest integer, is
21. When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 2.25 J2 then the value of R in Ω is
22. Two spherical bodies A (radius 6 cm ) and B(radius 18 cm ) are at temperature T1 and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?
23. When two progressive waves y1 = 4 sin(2x − 6t) and 
are superimposed, the amplitude of the resultant wave is
24. A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its crosssectional area is 4.9 × 10−7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s−1. If the Young’s modulus of the material of the wire is n × 109 Nm−2, the value of n is
25. A binary star consists of two stars A (mass 2.2Ms) and B (mass 11Ms), where Ms is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is
26. Gravitational acceleration on the surface of a planet is 
where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms−1, the escape speed on the surface of the planet in kms−1 will be
27. A piece of ice (heat capacity = 2100 J kg−1 °C−1 and latent heat = 3.36 ×105J kg−1) of mass m grams is at −5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is
28. A stationary source is emitting sound at a fixed frequency f0, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f0. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms−1.
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