A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just \(10 \%\) of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is.....\(^o\)

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. \(A.\) The electron will experience magnetic force along the axis of the solenoid. \(B.\) The electron will not experience magnetic force. \(C.\) The electron will continue to move along the axis of the solenoid. \(D.\) The electron will be accelerated along the axis of the solenoid. \(E.\) The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the options given below:

\(A, B, C\) and \(D\) are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \(AD = C\, ln\, (BD)\) holds true. Then which of the combination is not a meaningful quantity ?

An electric charge \(10^{-6} \mu \mathrm{C}\) is placed at origin \((0,0)\) \(\mathrm{m}\) of \(\mathrm{X}-\mathrm{Y}\) co-ordinate system. Two points \(\mathrm{P}\) and \(\mathrm{Q}\) are situated at \((\sqrt{3}, \sqrt{3}) \mathrm{m}\) and \((\sqrt{6}, 0) \mathrm{m}\) respectively. The potential difference between the points \(P\) and \(Q\) will be :

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at \(40\,cm\) from the pole of the mirror is formed at distance \(120\,cm\) from the pole of the mirror. These distances are measured with a modified scale in which there are \(20\) small divisions in \(1\,cm\). The value of error in measurement of focal length of the mirror is \(1 / K\) \(cm\). The value of \(K\) is  \(..........\)

A \(0.5 \,kg\) block moving at a speed of \(12 \,ms ^{-1}\) compresses a spring through a distance \(30\, cm\) when its speed is halved. The spring constant of the spring will be \(Nm ^{-1}\).

An \(AC\) source is connected to an inductance of \(100\,mH\) a capacitance of \(100\,\mu F\) and a resistance of \(120\,\Omega\) as shown in figure. The time in which the resistance having a thermal capacity \(2\,J^{\circ } C\) will get heated by \(16^{\circ} C\) is ..........\(S\)

An ac current is represented as
\(\mathrm{i}=5 \sqrt{2}+10 \cos \left(650 \pi \mathrm{t}+\frac{\pi}{6}\right) \mathrm{Amp}\)
The r.m.s value of the current is

A body of mass 4 kg is placed on a plane at a point P having coordinate \((3,4) \mathrm{m}\). Under the action of force \(\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}\), it moves to a new point Q having coordinates \((6,10) \mathrm{m}\) in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :

An alternating voltage source \(V =260 \sin (628\,t )\) is connected across a pure inductor of \(5\,mH\). Inductive reactance in the circuit is \(......... \Omega\)