• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, that you have to choose the correct one ( ONLY ONE ) from options given.

1. The radius of gyration of a disc is k and its radius is R. The ratio of R^{2} : k^{2} =

2. The ratio of RMS speed of a Hydrogen molecule to that of a Oxygen molecule, both at temperature 27^{0} C

SECTION II

This section contains 3( Three ) Questions

• Each question has 4 ( Four ) options : A, B, C and D. One or more than one of these four option(s) is(are) correct answer(s).

3. A projectile is thrown from ground with a velocity 10 ms^{-1}. Its horizontal range would be maximum when thrown at an angle of projection with horizontal is

4. The internal energy of an isolated thermodynamic system containing an ideal gas does not depend on a change in

5. Doppler effect is a phenomenon exhibited by

SECTION III

This section contains 10( Ten ) Questions

• Each question has 4 ( Four ) options : A, B, C and D. One of these four options is correct answer.

6. The distance covered by a body moving in a straight line along X-axis is given by x^{2} = t^{2} + 2t + 3. If its acceleration is given to vary as x^{n}, the value of n =

7. The minimum value of m in the system given, so that it remains in equilibrium will be

8. A spring of spring constant k is cut into 3:2 as per length. The spring constant of the longer part is

9. The transverse displacement of a string ( clamped at both ends ) is given by y (x,t) = 0.06 cos2πx/3 sin120πt where x and y are in meters and t is in seconds. The length of the string is 1.5m and its mass is 3 x 10^{-2} kg. The tension in the string is

10. A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force of F, its length increases by l. Another wire of same material of length 2L and radius 2r is pulled by a force 2F. The increase in the length of the wire is

11. The excess pressure inside the drop of a mercury of radius 3 mm is [ surface tension of mercury is 0.465 Nm^{-1} and atmospheric pressure is 1.014x10^{5} Pa ]

12. A particle executes simple harmonic motion with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from equilibrium position is

13. Which one of the following plots represents the variation of gravitational field on a particle with distance r due to thin spherical shell [ r is measured from centre of the
shell ]

14. Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular speeds will be

15. Match the accelerations (II) of the round bodies (I) rolling down an inclined plane of angle θ, given in two columns: