A beam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^o \) relative to that of \(A\). The intensity of the emergent light is _______.

A total of \(48 \mathrm{~J}\) heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by \(2^{\circ} \mathrm{C}\). The work done by the gas is _______. (Given, \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\).)

A cell \(E _{1}\) of \(emf 6 V\) and internal resistance \(2 \Omega\) is connected with another cell \(E _{2}\) of \(emf 4 V\) and internal resistance \(8 \Omega\) (as shown in the figure). The potential difference across points \(X\) and \(Y\) is............ \(V\)

A common transistor radio set requires \(12\,V (D.C.)\) for its operation. The \(D.C.\) source is constructed by using a transformer and a rectifier circuit, which are operated at \(220\, V\) \((A.C.)\) on standard domestic \(A.C.\) supply. The number of turns of secondary coil are \(24,\) then the number of turns of primary are

The angular momentum for the electron in Bohr's orbit is \(L\). If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

The surface tension of a soap bubble is \(0.03\) N/m. The work done in increasing the diameter of bubble from \(2\) cm to \(6\) cm is \(\alpha \pi \times 10^{-4}\) J. The value of \(\alpha\) is _______. (Take \(\pi = 3.14\))

A thin disc of radius \(b = 2a\)  has a concentric hole of radius \('a'\) in it (see figure). It carries uniform surface charge \('\sigma '\) on it. If the electric field on its axis at height \('h'\) \((h << a)\) from its centre is given as \('Ch'\) then value of \('C'\) is

The magnetic moment of an electron \((e)\) revolving in an orbit around nucleus with an orbital angular momentum is given by :

The temperature of \(3.00\, {mol}\) of an ideal diatomic gas is increased by \(40.0^{\circ} {C}\) without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is \(\frac{{x}}{10} .\) Then the value of \({x}\) (round off to the nearest integer) is ..... . \(\left(\right.\) Given \(\left.{R}=8.31\, {J} {mol}^{-1} {K}^{-1}\right)\)