Consider the situation shown in figure A spring of spring constant 400 N/m is attached at one end to a wedge fixed rigidly with the horizontal part. A 40 g mass is released form rest while situated at a height 5 cm the curved track. The minimum deformation in the spring is nearly equal to  

1. 9.8 m

2. 9.8 cm

3. 0.98 m

4. 0.009 km

A block having mass m collides with an another stationary block having mass 2 m. The lighter block comes to rest after collision. If the velocity of first block is v, then the value of coefficient of restitution will must be

1. 0.5

2. 0.4

3. 0.6

4. 0.8

A uniform sphere of mass 500 g rolls without slipping on a plane surface so that its centre moves at a speed of 0.02 m/s. 
The total kinetic energy of rolling sphere would be (in J)

1. $1.4\times {10}^{-4} J$

2. $0.75\times {10}^{-3} J$

3. $5.75\times {10}^{-3} J$

4. $4.9\times {10}^{-5} J$

The force on a particle as the function of displacement x(in x-direction) is given by 
F = 10 + 0.5 x 
The work done corresponding to displacement of particle from x = 0 to x = 2 unit is

1. 25 J

2. 29 J

3. 21 J

4. 18 J

The reading of a spring balance corresponds to 100 N while situated at the north pole and a body is kept on it. The weight record on the same scale if it is shifted to the equator, is 

1. 99.66 N

2. 110 N

3. 97.66 N

4. 106 N

If the intensity is increased by a factor of 20; then how many decibels in the sound level increased?

1. 18

2. 13

3. 9

4. 7

On the same path, the source and observer are moving such a ways that the distance between these two increases with the time. The speeds of source and observer are same and equal to  with respect to the ground while no wind is blowing. The apparent frequency received by observer is 1950 Hz then the original frequency must be (the speed of sound in present medium is 340 m/s)

1. 2068 Hz

2. 2100 Hz

3. 1903 Hz

4. 602 Hz

Consider the ray diagram for the refraction given below. The maximum value of angle θ for which the light suffers total internal reflection at the vertical surface, is 

1. ${\cos }^{-1}\left(\frac{3}{4}\right)$

2. ${\sin }^{-1}\left(\frac{3}{4}\right)$

3. ${\tan }^{-1}\left(\frac{4}{3}\right)$

4. ${\cos }^{-1}\left(\frac{4}{3}\right)$

The near point and far point of a person are 40 cm and 250 cm respectively. Determine the power of the lens he/she should use while reading a book kept at distance 25 cm from the eye.

1. 2.5 D

2. 5.0 D

3. 1.5 D

4. 3.5 D

The dimensional formula for electric flux is

1. [ ML³ I^-1 T^-3 ]

2. [ M² L² I^-1 T^-2 ]

3. [ ML³ I¹ T^-3 ]

4. [ ML^-3 I^-1 T^-3 ]