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Question Paper (Section wise)

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Question 1
Positive Marks: 4 / Negative Marks: 1
•  1) An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is Î¸, then:
•  2) A conducting circular loop made of a thin wire, has area 3.5 Ã— 10-3 m2 resistance 10 Î©. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4T) sin (50Ï€t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:
1. 0.14 mC

2. 0.77 mC

3. 0.21 mC

4. 0.6 mC

•  3) A parallel plate capacitor is made of two square plates of side â€˜a, separated by a distance d (d << a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is
•  4) The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as R1 has the colour code (Orange, Red, Brown) .The resistor R2 and R4 are 80 Î©, and 40 Î©, respectively. Assuming that the colour code for the carbon resistors, gives their accurate values, the colour code for the carbon resistor, used as R3 Would be
1. Brown, Blue, Brown

2. Brown, Blue, Black

3. Red, Green, Brown

4. Grey, Black, Brown

•  5) Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20Â°C to 90Â°C. Work done by has is close to: (Gas constant R= 8.31J/mol.K)
1. 581 J

2. 291 J

3. 146 J

4. 73 J

•  6) Two kg of a monoatomic gas is at a pressure of 4 Ã— 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion?
1. 103 J

2. 105 J

3. 104 J

4. 106 J

•  7) A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earthâ€™s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:
1. âˆš2gR

2. âˆšgR

3. âˆšgR(âˆš2 - 1)

•  8) A particle is moving along a circular path with a constant speed of 10 msâ€“1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60Â°+ around the centre of the circle?
1. 10âˆš3 m/s

2. 0

3. 10âˆš2 m/s

4. 10 m/s

•  9) An electromagnetic wave of intensity 50 Wmâ€“2 enters in a medium of refractive indexâ€™ nâ€™ without any loss . The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively. Given by:
1. (âˆšn, âˆšn)

•  10) To double the covering range of a TV transition tower, its height should be multiplied by:
1. 2

2. 4

3. âˆš2

•  11) A paramagnetic material has 1028 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 Ã— 10-4. Its susceptibility at 300 K is:
1. 3.267 Ã— 10-4

2. 3.672 Ã— 10-4

3. 3.726 Ã— 10-4

4. 2.672 Ã— 10-4

•  12) Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?
1. Image disappears

2. Magnified image

3. Erect real image

4. No change

•  13) In a simple pendulum experiment for determination of acceleration due to gravity (g), times taken for 20 oscillation is measured by using a watch of 1 second least count. The mean value of time the taken comes out to be 30s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. percentage error in the determination of g is close to:
1. 0.7%

2. 3.5%

3. 6.8%

4. 0.2%

•  14) An electric dipole is formed by two equal and opposite charges q with separation d. The charges the same mass m. It is kept in a uniform electric field E. If it slightly rotated from its equilibrium orientation, then its angular frequency Ï‰ is:
•  15) A circuit connected to an as source of emf e = e0 sin (1000t) with t in seconds, gives a phase difference of Â between the emf e and current i. Which of the following circuits will exhibit this?
1. RC circuit with R = 1 k Î© and C = 1 Î¼F

2. RL circuit with R = 1 k Î© and L = 10 mH

3. RL circuit with R = 1 k Î© and L = 1 mH

4. RC circuit with R = 1 kÎ© andÂ  C = 10Î¼F

•  16) A moving coil galvanometer has resistance 50 Ω and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a 5 kΩ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to:
1. 15 V

2. 20 V

3. 10 V

4. 40 V

•  17) A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:
1. 0.16 m

2. 1.60 m

3. 0.24 m

4. 0.32 m

•  18) A string is clamed at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y =0.3 sin (0.157x) cos (200Ï€t). The length of the string is: (all quantities are in SI units).
1. 80 m

2. 60 m

3. 40 m

4. 20 m

•  19) A plane is inclined at an angle Î± = 30Â° 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 Î¸ = 15Â° 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 Take g = 10 ms2
1. 18 cm

2. 14 cm

3. 26 cm

4. 20 cm

•  20) The time dependence of the position of a particle of mass m = 2 is given by Â its angular momentum with respect to the origin at time t = 2 is
•  21) A coil of self-inductance 10mH and resistance 0.1 Î© is connected through a switch to a battery of internal resistance 0.9 Î©. After the switch is closed the time taken for the current to attain 80% of the saturation values is ______ ms. [ take ln5 = 1.6]
•  22) Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). The approximate value of molar specific heat of mixture at constant volume is ______. (R = 8.3 J/mol K)
•  23) A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R form it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is _____Ã—.
•  24) To concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water field up to 5 cm (see its figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to _____ cm. (Refractive index of water = 1.33)
•  25) From a uniform circular disc of radius R and mass 9M, a small disc of radius  is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is ______×I0. (Here, I0 = MR2)
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