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# Question Paper (Section wise)

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Question 1
Positive Marks: 4 / Negative Marks: 1
•  1) A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is:
1. 1.1 cm away from the lens

2. 0

3. 0.55 cm towards the lens

4. 0.55 cm away from lens

•  2) A resistance is shown in the figure. Its value and tolerance are given respectively by:

•  3) A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, Â The corresponding magnetic field , at that point will be
•  4) Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (See figure.) The moment of inertia of system about the axis passing perpendicularly through the centre of the rod is:
•  5) Consider a Youngâ€™s double slit experiment as shown in figure. What should be the slit separation d in terms of Wavelength Î» such that the first minima occurs directly in front of the slit (S1)?
•  6) The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression. The magnetic field (x, z, t) is given by: (c is the velocity of light)
•  7) A body is projected at t = 0 with a velocity 10ms-1 at an angle of 60Â° with the horizontal. The radius of curvature of its trajectory at t=1s is R. Neglecting air resistance and taking acceleration due to gravity g=10 ms-2. The radius of R is
1. 10.3 m

2. 2.8 m

3. 2.5 m

4. 5.1 m

•  8) The force of interaction between two atoms is given by; where x is the distance, k is the Boltzmann constant and T is temperature and Î± and Î² are two constants. The dimension of Î² is:
1. M0L2T-4

2. M2LT-4

3. MLT-2

4. M2L2T-2

•  9) A body of mass 1 kg falls freely from a height of 100 m, on a platform of masses 3kg which is mounted on a spring having constant k = 1.25 Ã— 106 N/m. The body sticks to the platform and the springâ€™s maximum compression is found to be x. Given that g=10 ms-2 the value of x will be close to:
1. 40 cm

2. 4 cm

3. 80 cm

4. 2 cm

•  10) An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300K. The mean time between two successive collisions is 6 Ã— 10-8 s. if the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to:
1. 2 Ã— 10-7 s

2. 4 Ã— 10-8 s

3. 0.5 Ã— 10-8 s

4. 3 Ã— 10-6 s

•  11) A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms-1, at right angles to the horizontal component of the earthâ€™s magnetic of field, 0.3 Ã— 10-4 Wb/m2. The value of the induced emf in wire is:
1. 1.5 Ã— 10-3 V

2. 1.1 Ã— 10-3 V

3. 2.5 Ã— 10-3 V

4. 0.3 Ã— 10-3 V

•  12) The mean intensity of radiation on the surface of the sun is about 108 W/m2. The rms value of the corresponding magnetic field is closet to:
1. 1 T

2. 102 T

3. 10-2 T

4. 10-4 T

•  13) If Surface tension (S), Moment of Inertia (I) and Planckâ€™s constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:
1. S1/2I1/2h0

2. S1/2I3/2h-1

3. S3/2I1/2h0

4. S1/2I1/2h-1

•  14) Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing through their mid-point P, at angle Ñ² =45Â° with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimension of the dipole)
1. 0

•  15) A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (V) of the point charge, as a function of instantaneous distance r from line charge, it proportional to
•  16) The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: (i) a ring of radius R, (ii) a solid cylinder of radius and (iii) a solid sphere of radius . If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is:
1. 10: 15: 7

2. 20: 15: 14

3. 4: 3: 2

4. 2: 3: 4

•  17) A rectangular coil (Dimension 5 cm Ã— 2 cm) with 100 100 turns, carrying a current of 3 A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45Â° about Z-axis, then the torque on the coil is:
1. 0.42 Nm

2. 0.55 Nm

3. 0.27 Nm

4. 0.38 Nm

•  18) The magnetic field of a plane electromagnetic wave is given by: Where B0= 3 Ã— 10-5 T and B1 = 2 Ã—10-6 T. The rms value of the force experienced by a stationary charge Q = 10-4 = C at z = 0 is closet to:
1. 0.9 N

2. 0.6 N

3. 0.1 N

4. 3 Ã—10-2N

•  19) One mole of ideal gas passes through a process where pressure and volume obey the relation Here P0 and V0 are constant. Calculate the change in the temperature of the gas if its volume change from V0 to 2V0
•  20) The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz,
•  21) A 2 mW laser operates at a wavelength of 500 nm. The approximate number photons that will be emitted per second is ______ Ã— 1015. [Given Planckâ€™s constant h = 6.6 Ã— 10-34 Js, speed of light c = 3.0 Ã— 108 m/s]
•  22) An excited He+ ion emits two photons in succession, with wavelength 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is ______. (For photon of wavelength Î», energy )
•  23) The resistive network shown below is connected to a D. C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is _____ Î©.
•  24) An amplitude modulated waves is represented by expression vm = 5 (1 + 0.6 cos 6280t) sin (211 Ã— 104t) volts. The maximum amplitudes of the amplitude modulated wave is _______.
•  25) A galvanometer, whose resistance is 50 Î© has 25 divisions in it. When a current of 0.4 mA passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of ____ Î©.
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