Two polarisers \(P_1\) and \(P_2\) are placed in such a way that the intensity of the transmitted light will be zero. A third polariser \(P_3\) is inserted in between \(P_1\) and \(\mathrm{P}_2\), at the particular angle between \(\mathrm{P}_2\) and \(\mathrm{P}_3\). The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers \(\mathrm{P}_2\) and \(\mathrm{P}_3\) is :

The time taken for the magnetic energy to reach \(25\, \%\) of its maximum value, when a solenoid of resistance \(R ,\) inductance \(L\) is connected to a battery, is :

Choose the correct nuclear process from the below options.
[p: proton, n : neutron, \(\mathrm{e}^{-}\): electron, \(\mathrm{e}^{+}\): positron, \(v:\) neutrino, \(\bar{v}\) : antineutrino]

Figure shows a circuit in which three identical diodes are used . Each diode has forward resistance of \(20\,\Omega \) and infinite backward resistance. Resistors \(R_1 = R_2 = R_3 = 50\,\Omega.\) Battery voltage is \(6\,V.\) The current through \(R_3\) is.....\(mA\)

A particle of mass \(m\) is moving with speed \(2\, v\) collides with a mass \(2\,m\) moving with speed \(v\) in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass \(m\), which move at angle \(45^o\) with respect to the original direction. The speed of each of the moving particle will be

An observer looks at a distant tree of height \(10\ m\) with a telescope of magnifying power of \(20\). To the observer the tree appears :

A ball of mass \(10\, kg\) moving with a velocity \(10 \sqrt{3}\, ms ^{-1}\) along \(X-\)axis, hits another ball of mass \(20\, kg\) which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along \(Y-\) axis at a speed of \(10\, m / s\). The second piece starts moving at a speed of \(20\, m / s\) at an angle \(\theta\) (degree) with respect to the \(X-\)axis. The configuration of pieces after collision is shown in the figure. The value of \(\theta\) to the nearest integer is

If \(10^{22}\) gas molecules each of mass \(10^{-26}\, kg\) collide with a surface (perpendicular to it)elastically per second over an area \(1\, m^2\) with a speed \(10^4\,m/s\), the pressure exerted by the gas molecules will be of the order of

An electron with mass ' \(m\) ' with an initial velocity \((\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}} \quad\left(\mathrm{v}_0 \gt 0\right)\) enters a magnetic field \(\vec{B}=B_0 \hat{j}\). If the initial de-Broglie wavelength at \(\mathrm{t}=0\) is \(\lambda_0\) then its value after time ' t ' would be :

An electron of mass \(m\) and a photon have same energy \(E.\) The ratio of de-Broglie wavelengths associated with them is