A ball is released from a certain height which losses 50% of its kinetic energy on striking the ground, it will attain a height again of:
1. \(\frac14\)th of the initial height
2. \(\frac12\)th of the initial height
3. \(\frac34\)th of the initial height
4. None of the above

If applied torque on a system is zero, i.e., \(\tau=0\), then for that system:
1. \(\omega=0\)
2. \(\alpha=0\)
3. \(K.E=0\)
4. \(F=0\)

A steel wire of \(1~\mathrm{m}\) long and \(1~\mathrm{mm^2}\) cross-section area is hanged from a rigid end when the weight of \(1~\mathrm{kg}\) is hung from it, then the change in the length will be:
(Young’s coefficient for wire \(\mathrm{Y}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\))
1. \( 0.5 \mathrm{~mm} \)
2. \(0.25 \mathrm{~mm} \)
3. \(0.05 \mathrm{~mm} \)
4. \(5 \mathrm{~mm}\)

When plate voltage in diode valve is increased from 100 V to 150 V. Then, the plate increases from 7.5 mA to 12 mA, then dynamic plate resistance will be:
1. \(10~\mathrm{k\Omega}\)
2. \(11~\mathrm{k\Omega}\)
3. \(15~\mathrm{k\Omega}\)
4. \(11.1~\mathrm{k\Omega}\)

If the sun rays are indenting at \(60^\circ\) angle and intensity is \(I.\) If the sun rays are made incident at \(30^\circ\) angle, then what will be the intensity?
1. \(\frac{I}{\sqrt3}\)
2. \(\sqrt3 I\)
3. \(3I\)
4. \(\frac{I}{3}\)

The reason for current flow in the p-n junction in forward bias is:

A charged particle is accelerated by a potential of 200 V. If its velocity is 8.4 × 10⁸ m/s, then the value of e/m for that particle is:
1. 17.6 × 10¹⁶
2. 14.5 × 10¹²
3. 1.76 × 10¹⁵
4. 1.45 × 10¹⁵

When an open organ is dipped in water up to half of its height, then its frequency will become:
1. half
2. double
3. remain same
4. four times

A sound source producing waves of frequency 300 Hz and wavelength 1 m observer is stationary, while the source is going away with the velocity 30 m/s, then apparent frequency heard by the observer is:

1. 270 Hz

2. 273 Hz

3. 383 Hz

4. 300 Hz

A particle moves towards east for 2 s with velocity 15 m/s and move towards north for 8 s with velocity 5 m/s. Then, the average velocity of the particle is:

1. 2 m/s

2. 5 m/s

3. 7 m/s

4. 10 m/s