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# Question Paper (Section wise)

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Question 1
Positive Marks: 4 / Negative Marks: 1
•  1) A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds , is close to:
1. 3.16

2. 0.32

3. 0.45

4. 2.24

•  2) A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:
1. 1.0 × 10-7 T

2. 1.5 × 10-7 T

3. 1.5 × 10-5 T

4. 1.0 × 10-5 T

•  3) Three charges +Q, q, +Q are placed respectively, at distance 0, d/2 and d from the origin, on the x-axis. If the net force experienced by +Q, placed at x = 0, is zero, then value of q is
1. -Q/4

2. +Q/2

3. +Q/4

4. -Q/2

•  4) An unknown metal of mass 192 g heated to a temperature of 100Â°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4Â°C. Calculated the specific heat of the unknown metal if water temperature stabilized at 21.5Â°C. (Specific heat of brass is 394 J kg-1k-1).
1. 458 J kg-1K-1

2. 919 J/Kg K-1

3. Th = 1.5Tc

4. Th = 0.5c

•  5) The self-produce emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1 s, the change in the energy of the inductance is:
1. 740 J

2. 437.5 J

3. 540 J

4. 637.5 J

•  6) A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is:
1. 692 pJ

2. 508 pJ

3. 560 pJ

4. 600 pJ

•  7) A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980 Ã…. The radius of the atom in the excited state, in terms of Bohr radius a0, will be (hc = 12500 eV-Ã…)
1. 25a0

2. 9a0

3. 16a0

4. 4a0

•  8) A particle undergoing simple harmonic motion has time dependent displacement given by . The ratio of kinetic to potential energy of the particle at t = 210s will be
1. 1/9

2. 1

3. 2

4. 1/3

•  9) The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following, graph is the correct one, if Dm is the angle of minimum deviation?
•  10) A plano-convex lens (focal length f2, refractive index Âµ2, radius of curvature R) fits exactly into a plano- concave lens (focal length f1, refractive index Âµ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:
1. f1 â€“ f2

2. f1 + f2

•  11) A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is l1, and that below the piston is l2, such that l1 > l2. Each part of the cylinder contains n moles of an ideal gas at equal temperature. T. (R is universal gas constant and g is the acceleration due to gravity)
•  12) In a Frank-hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to:
1. 1700 nm

2. 2020 nm

3. 220 nm

4. 250 nm

•  13) A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at same position even if the concave mirror, by itself would produce a virtual image would be:
1. 20 cm

2. 10 cm

3. 30 cm

4. 20 cm

• 14)

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x â€“ axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

Â

 a. b. c. d.

1. a, b, c

2. A

3. b, c

4. a, b, d

•  15) The given diagram shows four processes i.e., isochoric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:
1. a d c d

2. a d b c

3. d a c b

4. d a b c

•  16) An NPN transistor is used in common emitter configuration as an amplifier with 1 kÎ© load resistance. Signal voltage of 10 mV is applied across the base-emitter. This produces a 3 mA change in the collector current and 15 Î¼A change in the base current of the amplifier. The input resistance and voltage gain are:

•  17) Following figure shows two processes A and B for a gas. If âˆ†QA and âˆ†QB are the amount of heat absorbed by the system in two cases, and âˆ†UA and âˆ†UB are changes in internal energies, respectively, then:
1. âˆ†QA = âˆ†QB; âˆ†UA = âˆ†UB

2. âˆ†QA > âˆ†QB; âˆ†UA = âˆ†UB

3. âˆ†QA < âˆ†QB; âˆ†UA < âˆ†UB

4. âˆ†QA > âˆ†QB; âˆ†UA > âˆ†UB

•  18) A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of Î¸, where Î¸ is the angle by which it has rotated, is given as kÎ¸2. If its moment of inertia is I then the angular acceleration of the disc is:
•  19) A bullet of mass 20 g has an initial speed of 1 ms-1 just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers mean resistance of 2.5 Ã— 10-2 N, the speed of the bullet after emerging from the other side of the wall is close to
1. 0.7 ms-1

2. 0.3 ms-1

3. 0.1 ms-1

4. 0.4 ms-1

•  20) In free space, a particle A of charge 1 Âµ C is held fixed at a point P. Another particle B of the same charge and mass 4 Âµg is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is
1. 1.5 Ã— 102 m/s

2. 2.0 Ã— 103 m/s

3. 1.0 m/s

4. None

•  21) A source of sound S is moving with the velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the sound as 1000Hz. The apparent frequency of the source when it is moving away from the observer after crossing him is ______. (Take velocity of sound in air is 350 m/s)
•  22) What will be value of x in the given equation below which is used to express dimension of resistance? (Here, R is electrical resistance, âˆˆ0 is the permittivity of vacuum and Î¼0 is the permeability of vacuum)
•  23) Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be. The angle between polarizer A and C is ________Â°.
•  24) A spaceship orbits around a planet at a height of 20 km from surface. Assuming that only gravitational field of the plant acts on the spaceship. The approximate number of revolution made by the spaceship in 24 hours around the plane is ______. [Given: Mass of plane = 8 Ã— 1022 kg, Radius of planet = 2 Ã— 106 m, Gravitational constant G = 6.67 Ã— 10-11 Nm2/kg2]
•  25) A plane is inclined at an angle α = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms-1, from the base of the plant, making an angle θ = 15° with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to ______ cm. (Take, g = 10 m/s2)
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