A \(12\,V\) battery connected to a coil of resistance \(6 \,\Omega\) through a switch, drives a constant current in the circuit. The switch is opened in \(1\,ms\). The emf induced across the coil is \(20 \;V\). The inductance of the coil is  ........... \(mH\)

A system of three polarizers \(P_1, P_2, P_3\) is set up such that the pass axis of \(P_3\) is crossed with respect to that of \(P_1\). The pass axis of \(P_2\) is inclined at \(60^o\) to the pass axis of \(P_3\). When a beam of unpolarized light of intensity \(I_0\) is incident on \(P_1\), the intensity of light transmitted by the three polarizers is \(I\). The ratio \((I_0/I)\) equals (nearly)

Choose the correct statement for processes \(A\)  & \(B\) shown in figure.

The logic gate equivalent to the given circuit diagram is:

A circular disc of mass \(M\) and radius \(R\) is rotating about its axis with angular speed \(\omega_{1}\) If another stationary disc having radius \(\frac{ R }{2}\) and same mass \(M\) is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_{2}\). The energy lost in the process is \(p \%\) of the initial energy. Value of \(p\) is

Two simple harmonic motion, are represented by the equations \({y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)\) \(y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)\) Ratio of amplitude of \({y}_{1}\) to \({y}_{2}={x}: 1\). The value of \({x}\) is ...... .

Match List-\(I\) with List-\(II\) :-

List - \(I\) (EM-Wave)	List - \(II\) (Wavelength) (Range)
\((A)\) infra-red	\((i)\) \(<10^{-3} \mathrm{~nm}\)
\((B)\) Ultraviolet	\((ii)\) \(400 \mathrm{~nm}\) to \(1 \mathrm{~nm}\)
\((C)\) X-rays	\((iii)\) \(1 \mathrm{~mm}\) to \(700 \mathrm{~nm}\)
\((D)\) Gamma rays	\((iv)\) \(1 \mathrm{~nm}\) to \(10^{-3} \mathrm{~nm}\)

Choose the correct answer from the options given below:

A particle \((\mathrm{m}=1\; \mathrm{kg})\) slides down a frictionless track \((AOC)\) starting from rest at a point \(A\) (height \(2\; \mathrm{m}\) ). After reaching \(\mathrm{C}\), the particle continues to move freely in air as a projectile. When it reaching its highest point \(P\) (height \(1 \;\mathrm{m}\) ). the kinetic energy of the particle (in \(\mathrm{J}\) ) is : (Figure drawn is schematic and not to scale; take \(\left.g=10 \;\mathrm{ms}^{-2}\right)\)

Shown in the figure are two point charges \(+Q\) and \(-Q\) inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If \(\sigma _1\) is the surface charge on the inner surface and \(Q_1\) net charge on it and \(\sigma _2\) the surface charge on the outer surface and \(Q_2\) net charge on it then

If \(\vec{A}\) and \(\vec{B}\) are two vectors satisfying the relation \(\vec{A} . \vec{B}=[\vec{A} \times \vec{B}]\). Then the value of \([\vec{A}-\vec{B}]\). will be :

The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation.