A huge circular arc of length \(4.4\) \(ly\) subtends an angle \('4 {s}'\) at the centre of the circle. How long it would take for a body to complete \(4\) revolution if its speed is \(8 \;AU\;per\, second \;?\) Given : \(1\, {ly}=9.46 \times 10^{15} \,{m},\) \(\, {AU}=1.5 \times 10^{11}\, {m}\)

For the \(LCR\) circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor \(C '\) , when joined with the capacitor \(C\) present in the circuit , makes the power factor of the circuit unity. The capacitor \(C'\), must have been connected in

Given below are two statements: Statement \(I:\) A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. Statement \(II:\) A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below.

The distance between object and its two times magnified real image as produced by a convex lens is \(45 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :

Solid sphere \(A\) is rotating about an axis \(PQ\). If the radius of the sphere is \(5\,cm\) then its radius of gyration about \(P Q\) will be \(\sqrt{x} \;cm\). The value of \(x\) is \(................\).

In an electromagnetic wave the electric field vector and magnetic field vector are given as \(\vec{E}=E_{0} \hat{i}\) and \(\vec{B}=B_{0} \hat{k}\) respectively. The direction of propagation of electromagnetic wave is along.

Match List \(I\) with List \(II\)

List \(I\)	List \(II\)
\((A)\) Young's Modulus \((Y)\)	\((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\)
\((B)\) Co-efficient of Viscosity \((\eta)\)	\((II)\) \(\left[ M L ^2 T ^{-1}\right]\)
\((C)\) Planck's Constant \((h)\)	\((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\)
\((D)\) Work Function \((\phi)\)	\((IV)\) \(\left[ M L ^2 T ^{-2}\right]\)

Choose the correct answer from the options given below:

Suppose a uniformly charged wall provides a uniform electric field of \(2 \times 10^4 \mathrm{~N} / \mathrm{C}\) normally. A charged particle of mass \(2 \mathrm{~g}\) being suspended through a silk thread of length \(20 \mathrm{~cm}\) and remain stayed at a distance of \(10 \mathrm{~cm}\) from the wall. Then the charge on the particle will be \(\frac{1}{\sqrt{\mathrm{x}}} \ \mu \mathrm{C}\) where \(\mathrm{x}=\) _______ [use \(g=10 \mathrm{~m} / \mathrm{s}^2\)]

A bullet of mass \(50 \mathrm{~g}\) is fired with a speed \(100 \mathrm{~m} / \mathrm{s}\) on a plywood and emerges with \(40 \mathrm{~m} / \mathrm{s}\). The percentage loss of kinetic energy is _______.

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.