An inductor (L = 20 H), a resistor (R = 100 \(\Omega\)) and a battery (E = 10 V) are connected in series. After a long time, the circuit is short-circuited and then the battery is disconnected. Find the current in the circuit at 1 ms after short-circuiting.

1.  4.5 x 10⁶ A
2.  3.2 x 10^-5 A
3.  9.8 x 10^-6 A
4.  6.7 x 10^-4 A

A particle is subjected to two simple harmonic motions along the X-axis while the other is along a line making an angle of 45° with the X-axis. The two motions are given by \(x = x_0\) sin \(\omega t\) and \(s = s_0\) sin \(\omega t\). The amplitude of the resultant motion is:
1. \(x_0+s_0+2x_0s_0\)
2. \(\sqrt{x^2_0+s^2_0}\)
3. \(\sqrt{x^2_0+s^2_0+2x_0s_0}\)
4. \(x^2_0=s^2_0+\sqrt2x_0s_0~^{1/2}\)

What is the change in the volume of \(1.0~\mathrm{L}\) kerosene when it is subjected to an extra pressure of \(2.0 \times 10^5 \mathrm{~Nm}^{-2}\) from the following data?
(The density of kerosene \(=800~\mathrm{kgm^3}\) and the speed of sound in kerosene \(=1330~\mathrm{ms^{-1}}\))
1. \( 0.97 \mathrm{~cm}^{-3} \)
2. \( 0.66 \mathrm{~cm}^{-3} \)
3. \( 0.15 \mathrm{~cm}^{-3} \)
4. \(0.59 \mathrm{~cm}^{-3}\)

Water level is maintained in a cylindrical vessel up to a fixed height \(H.\) The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel? 

1. \(h=\frac{H}{2}\)
2. \(h=\frac{3H}{2}\)
3. \(h=\frac{2H}{3}\)
4. \(h=\frac{3}{4}H\)

The figure shows a spring + block + pulley system which is light. The time period of mass would be:

1. \(2\pi\sqrt{\frac{k}{m}}\)
2. \(\frac{1}{2\pi}\sqrt{\frac{k}{m}}\)
3. \(2\pi\sqrt{\frac{m}{k}}\)
4. None of these