The wavelength of the photon emitted by a hydrogen atom when an electron makes a  transition from \(n =2\) to \(n =1\) state is ...... \(nm.\)

A steel wire with mass per unit length \(7.0 \times 10^{-3}\,kg\,m ^{-1}\) is under tension of \(70\,N\). The speed of transverse waves in the wire will be \(.........m/s\)

One mole of an ideal gas at \(27^{\circ} {C}\) is taken from \({A}\) to \({B}\) as shown in the given \({PV}\) indicator diagram. The work done by the system will be \(......\times 10^{-1} \,{J}\) [Given : \(R=8.3\, {J} /\,mole\,{K}, \ln 2=0.6931\) ] (Round off to the nearest integer)

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance \(C\) will be

A homogeneous solid cylindrical roller of radius \(R\) and mass \(M\) is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

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

List\(-I\)	List\(-II\)
\((A)\) Angular momentum	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) Torque	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) Stress	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) Pressure gradient	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

Choose the correct answer from the options given below:

In the Young's double slit experiment, the distance between the slits varies in time as \({d}({t})={d}_{0}+{a}_{0}\, sin\omega \,t\) ; where \({d}_{0}, \omega\) and \(a_{0}\) are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

A velocity selector consists of electric field \(\overrightarrow{ E }= E \hat{ k }\) and magnetic field \(\overrightarrow{ B }= B \hat{ j }\) with \(B =12 mT\). The value \(E\) required for an electron of energy \(728 eV\) moving along the positive \(x\)-axis to pass undeflected is: (Given, , ass of electron \(=9.1 \times 10^{-31} kg\) )

A gas mixture consists of \(3\) moles of oxygen and \(5\) moles of argon at temperature \(T\). Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of \(RT\) ) of the mixture is

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :