PART I : PHYSICS
SECTION I : (Only One option correct Type)
This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1. The work done on a particle of mass m by a force, 
(K being a constant of appropriate dimension), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is
(A) 
(B) 
(C) 
(D) 
2. Two rectangular block, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the block has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is
(A) 2.0 s
(B) 3.0 s
(C) 4.5 s
(D) 6.0 s
3. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is
(A) 1 : 4
(B) 1 : 2
(C) 6 : 9
(D) 8 : 9
4. A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is
(A) 
(B) 
(C) 
(D) 
5. A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 108 ms−1. The final momentum of the object is
(A) 0.3 × 10−17 kg ms−1
(B) 1.0 × 10−17 kg ms−1
(C) 3.0 × 10−17 kg ms−1
(D) 9.0 × 10−17 kg ms−1
6. In the Young’s double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is
(A) 
(B) 
(C) 
(D) 
7. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 
the wavelength in free space. The radius of the curved surface of the lens is
(A) 1 m
(B) 2 m
(C) 3 m
(D) 6 m
8. One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
(A) 0.25
(B) 0.50
(C) 2.00
(D) 4.00
9. A ray of light travelling in the direction 
is incident on a plane mirror. After reflection, it travels along the direction
. The angle of incidence is
(A) 30°
(B) 45°
(C) 60°
(D) 75°
10. The diameter of a cylinder is measured using a Vernier caliper with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is
(A) 5.112 cm
(B) 5.124 cm
(C) 5.136 cm
(D) 5.148 cm
SECTION II : (One or more options correct Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B),(C) and (D) out of which ONE or MORE are correct.
11. In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time,
(A) the charge on the upper plate of C1 is 2CV0.
(B) the charge on the upper plate of C1 is CV0.
(C) the charge on the upper plate of C2 is 0.
(D) the charge on the upper plate of C2 is −CV0.
12. A particle of mass M and positive charge Q, moving with a constant velocity 
enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity 
The correct statement(s) is (are)
(A) The direction of the magnetic field is −z direction.
(B) The direction of the magnetic field is +z direction.
(C) The magnitude of the magnetic field 
(D) The magnitude of the magnetic field is 
13. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m−1)x]. cos[(628 s−1)t]. Assuming π = 3.14, the correct statement(s) is (are)
(A) The number of nodes is 5.
(B) The length of the string is 0.25 m.
(C) The maximum displacement of the midpoint of ht string, from its equilibrium position is 0.01 m.
(D) The fundamental frequency is 100 Hz.
14. A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are)
(A) the net elongation of the spring is 
(B) the net elongation of the spring is 
(C) the light sphere is partially submerged.
(D) the light sphere is completely submerged.
15. Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ1 and ρ2 respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio 
can be
(A) −4
(B) 
(C) 
(D) 4
SECTION III : (Integer value correct Type)
This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
16. A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio 
is
Answer: (5)
17. A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms−1) of the particle is zero, the speed (in ms−1) after 5 s is
18. The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is
19. A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ℓn 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is
20. A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s−1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s−1) of the system is
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