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# Question Paper (Section wise)

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Question 1
Positive Marks: 4 / Negative Marks: 1
•  1) A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s2 at a distance of 5 m from the mean position. The time period of oscillation is
1. 2 s

2. π s

3. 2π s

4. 1 s

•  2) An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is.
1. 10 times greater

2. 5 times greater

3. Smaller

4. Equal

•  3) An electron of mass m with an initial velocity enters an electric fie at t = 0. If λ0 its de-Broglie wavelength initially, then de- Broglie wavelength initially, then de-Broglie wavelength at time is
1. λ0t

2. 3. 4. λ0

•  4) For a radioactive material, half -life 10 minutes. If initially there are 600 number nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
1. 30

2. 10

3. 20

4. 15

•  5) When the light of frequency 2ν0 (where ν0 threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v1. When the frequency of the incident radiation is increased to 5ν0, the maximum velocity of electrons emitted from the same plate is v2. The ratio of v1 to v2 is
1. 4 : 1

2. 1 : 4

3. 1 : 2

4. 2 : 1

•  6) The ratio of kinetic energy to the total energy an electron in a Bohr orbit of the hydrogen atomic is
1. 2 : -1

2. 1 : -1

3. 1 : 1

4. 1 : -2

•  7) An em wave is propagating in a medium with a velocity. The instantaneous oscillating electric field of this em wave is along +y axis. Then the direction of oscillating magnetic field of the em wave will be along.
1. -y direction

2. +z direction

3. -z direction

4. -x direction

•  8) The refractive index of the material of a prism is and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is -
1. 30°

2. 45°

3. 60°

4. Zero

•  9) The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance
1. 1.389 H

2. 138.88 H

3. 0.138 H

4. 13.89 H

•  10) The diagram below show regions of equipotential. A positive charge is moved from A to B in each diagram.
1. In all the four cases the work done is the same.

2. Minimum work is required to move q in figure (a)

3. Maximum work is required to move in q in figure (b)

4. Maximum work is required to move in q in figure (c)

•  11) Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:
1. move towards each other

2. move away from each other

3. will become stationary

4. keep floating at the same distance between them

•  12) The x and y coordinates of the particle at any time are x = 5t – 2t2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t= 2s is:
1. 5 m/s2

2. - 4 m/s2

3. - 8 m/s2

4. 0

•  13) One end of string of length is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards center) will be (T represents the tension in the string)
1. 2. 3. Zero

4. T

•  14) A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:
1. 2. 3. 4. •  15) Two Polaroids P1 and P2 are placed with their axis perpendicular to each other. Unpolarized light I0 is incident on P1. A third polaroid P3 is kept in between P1 and P2 such that axis makes an angle 45° with that of P1. The intensity of transmitted light through P2 is:
1. 2. 3. 4. •  16) The bulk modulus of spherical object is ‘B’ If it is subjected to uniform pressure ‘p’ , the fractional; deceases in radius is:
1. 2. 3. 4. •  17) In an electromagnetic wave in free space the root mean square value of the electric field is Erms = 6V/m. The peak value of the magnetic field is:
1. 2.83 × 10-8T

2. 0.70 × 10-8T

3. 4.23 × 10-8T

4. 1.41 × 10-8T

•  18) A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?

3. 5 m/s2

4. 25 m/s2

•  19) A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?
1. mKT

2. P/ (kT)

3. Pm / (kT)

4. P / (kTV)

•  20) A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg. The time period of oscillations becomes 5s. The value of m in kg is
1. 2. 3. 4. •  21) The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L meter long. The length of the open pipe will be
1. 4 L

2. L

3. 2 L

4. •  22) Three sound waves of equal amplitudes have frequencies (n – 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be
1. 2

2. 1

3. 4

4. 3

•  23) An electric dipole is placed at an angle of 30° with an electric field intensity 2 × 105 N/C. it experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is
1. 4 μ C

2. 5 mC

3. 2 mC

4. 5 mC

•  24) A parallel – plate capacitor of area A, plate separation d and capacitance C is file with four dielectric materials having dielectric constants k1, k2, k3 and k4 as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in the capacitor. Then its dielectric constant k is given by 1. 2. k = k1 + k2 + k3 + 3k4

3. 4. •  25) The potential difference (VA - VB)between the points A and B, where I=2A in the given figure is 34 1. + 9 V

2. - 3 V

3. + 3 V

4. + 6 V

•  26) A filament bulb (500W, 100V) is to be used in a 230 V main supply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. the value of R is
1. 13 Ω

2. 230 Ω

3. 46 Ω

4. 26 Ω

•  27) A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the loop is B. it is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be
1. 2n2 B

2. nB

3. n2 B

4. 2nB

•  28) What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?
1. √gR

2. √2gR

3. √3gR

4. √5gR

•  29) When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is . The threshold wavelength for the metallic surface is:
1. •  30) A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
1. Compressing the gas isothermally will require more work to be done.

2. Compressing the gas through adiabatic process will require more wore to be done.

3. Compressing the gas isothermally or adiabatically will require the same amount of work.

4. Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

•  31) A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then it opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emf’s is:
1. 5 : 1

2. 5 : 4

3. 3 : 4

4. 3 : 2

•  32) An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:
1. 37.3 cm

2. 46.0 cm

3. 50.0 cm

4. 54.0 cm

•  33) Two non–mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p < 1) in the denser liquid. The density d is equal to:
1. {1 + (n + 1) p} ρ

2. {2 + (n + 1) p} ρ

3. {2 + (n - 1) p} ρ

4. {1 + (n - 1) p} ρ

•  34) To get output 1 for the following circuit, the correct choice for the input is: 1. A = 0, B = 1, C = 0

2. A = 1, B = 0, C = 0

3. A = 1, B = 1, C = 0

4. A = 1, B = 0, C = 1

•  35) A piece of ice falls from a height h so that it melts completely. Only one–quarter of the heat produced is observed by the ice and all energy of ice gets converted into heat during its fall. The value of h is: [Latent heat of ice is 3.4 × 105J/kg and g = 10 N/kg]
1. 34 km

2. 544 km

3. 136 km

4. 68 km

•  36) The ratio of escape velocity at earth (ve) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is:
1. 1 : 2

2. 1: 2√2

3. 1 : 4

4. 1 : √2

•  37) A circuit contains an ammeter, a battery of 30 V and a resistance 40.8 ohm all connected in series. If the ammeter has a coil of resistance 480 ohm and a shunt of 20 ohm, the regarding in the ammeter will be-
1. 0.5 A

2. 0.25 A

3. 2 A

4. 1 A

•  38) The value of coefficient if volume expansion of glycerin is 5 × 10-4 K-1. The fractional change in the density of glycerin for a rise of 40°C in its temperature is-
1. 0.015

2. 0.020

3. 0.025

4. 0.010

•  39) The heart of a man pumps 5 litres of blood trough the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 ×103kg/m3 and g = 10 m/s2 then the power of heart in watt is-
1. 1.70

2. 2.25

3. 3.0

4. 1.50

•  40) A beam of light consisting of red, green and blue colours is incident on right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.444 and 1.47, respectively. 1. separate the blue colour part from the red and green colours

2. separate all the three colours from one another

3. not-separate the three colours at all

4. separate the red colour part from the green and blue colours

•  41) A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Weber/m2. The coli carries a current of 2A. If the plane of the coil is inclined at an angle of 30° with the direction of the field, the torque required to keep the coil in stable equilibrium will be;
1. 0.15 Nm

2. 0.20 Nm

3. 0.24 Nm

4. 0.12Nm

•  42) An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil? 1. Abcd

3. The current will revers its direction as the electron goes past the coil

4. No current induced

•  43) A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:
1. The helium nucleus has more kinetic energy than the thorium nucleus.

2. The helium nucleus has les momentum then the thorium nucleus.

3. The helium nucleus has more momentum than the thorium nucleus.

4. The helium nucleus has less kinetic energy than the thorium nucleus.

•  44) A for is acting at a point . The value of α for which an angular momentum about origin is conserved is:
1. -1

2. 2

3. Zero

4. 1

•  45) Water rises to a height ‘h’ in capillary tube. If the length of capillary tube above the surface of water is made less than ‘h’, then:
1. water rises upto the tip of capillary tube and then stars overflowing like a fountain.

2. water rises upto the top of capillary tube and stays there without overflowing.

3. water rises upto a point a little below the top and stays there.

4. water does not rises at all.

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