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# Question Paper (Section wise)

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Question 1
Positive Marks: 4 / Negative Marks: 1
•  1) For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of is:
1. 2. 3. R

4. R√2

•  2) Two coherent source produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:
1. 16 : 9

2. 25 : 9

3. 4 : 1

4. 5 : 3

•  3) Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length , is connected across AB (see figure). In steady state, temperature difference between P and Q will be closed to: 1. 45°C

2. 75°C

3. 60°C

4. 35°C

•  4) Two vectors have equal magnitudes. The magnitude of is ‘n‘ times the magnitude of . The angle between is:
1. 2. 3. 4. •  5) The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculated the distance from the refracting surface at which a parallel beam of light will come to focus.
1. 1 cm

2. 2 cm

3. 4.0 cm

4. 3.1 cm

•  6) A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be: (Assume that the highest frequency a person can hear is 20,000 Hz).
1. 6

2. 4

3. 7

4. 5

•  7) The equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the mid points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:
1. 2. 3. 4. •  8) Ice at –20° C is added to 50 g of water at 40° C. When the temperature of the mixture reaches 0° C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/°C) Heat of fusion of water at 0°C = 334 J/g)
1. 50g

2. 100g

3. 60g

4. 40g

•  9) A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is:
1. 15 RT

2. 12 RT

3. 4 RT

4. 20 RT

•  10) In the figure, given that VBB supply can vary from 0 to 5.0 VCC = 5 V, βdc = 200, RB = 100 kΩ, Rc =1kΩ an VBE = 1.0 V, The minimum base current and the input voltage at which the transistor will go to saturation, will be respectively: 1. 25 µA and 3.5 V

2. 20 µA and 3.5 V

3. 25 µA and 2.8 V

4. 20 µA and 2.8 V

•  11) A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:
1. 2.0

2. 0.1

3. 0.4

4. 1.2

•  12) A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be: [Take g = 10 m/s2] 1. 2 kg-m2/s

2. 8 kg-m2/s

3. 6 kg-m2/s

4. 3 kg-m2/s

•  13) A damped harmonic oscillator has a frequency of 5 oscillations per seconds. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to of the original amplitude is closed to:
1. 10 s

2. 100 s

3. 50 s

4. 20 s

•  14) The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity form the earth is closest to: [Boltzman’s Constant kB = 1.38 × 10-23 J/k Avogadro number N˄ = 6.02 × 1026 / kg Radius of Earth: 6.4 × 106 m Gravitation acceleration on Earth = 10 ms2]
1. 800k

2. 104 K

3. 3 × 105

4. 650 K

•  15) In the figure shown, what is the current (in Ampere) drawn from the battery? You are given R1 = 15Ω, R2 = 10 Ω, R3 = 20Ω, R4 = 5Ω, R5 = 25Ω, R6 = 30Ω, E = 15V 1. 13/24

2. 7/18

3. 9/32

4. 20/3

•  16) A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such that its part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface, the work done should be:
1. nMgL

2. 3. 4. •  17) A ball is thrown vertically up (taken as + z-axis) from the ground. The correct momentum height (p-h) diagram is:
1. 2. 3. 4. •  18) A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD) 1. 2. 3. 4. R

•  19) A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let l1 be the moment of inertia of the disc about its axis and l2 be the moment of inertia of the new sphere about its axis. The ratio of l1/l2 is given by:
1. 285

2. 185

3. 65

4. 140

•  20) A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotation per second is 5 s is close to 1. 2.0 × 10-5 Nm

2. 4.0 × 10-6 Nm

3. 1.6 × 10-5 Nm

4. 7.9 × 10-6 Nm

•  21) The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of 1 cms-1 At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of the loop. If the resistance of L is 1.7 Ω, the current in the loop at that instant will be close to _____ μA. •  22) A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the approximate value of B1 is _____ T, when B2 is 50 T.
•  23) The trajectory of a projectile near the surface of the earth is given as y =x – 9x2. For the given case the angle of projection with respect to ground is _____ °.
•  24) A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle’s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is ______ mm.
•  25) An alpha-particle of mass m suffers 1-deminisional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is ______×m.
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