A copper rod of cross-sectional area \(A\) carries a uniform current \(I\) through it. At temperature \(T\), if the volume charge density of the rod is \(\rho \), how long will the charges take to travel a distance \(d\) ?

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and \(2 \sqrt{3}\) (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is _________ .

As shown in figure, a cuboid lies in a region with electric field \(E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C\). The magnitude of charge within the cuboid is \(n \varepsilon_0 C\). The value of \(n\) is \(............\) (if dimension of cuboid is \(1 \times 2 \times 3 \;m ^3\) )

An ideal transformer with purely resistive load operates at \(12\,kV\) on the primary side. It supplies electrical energy to a number of nearby houses at \(120\,V\). The average rate of energy consumption in the houses served by the transformer is \(60\,kW\). The value of resistive load (Rs) required in the secondary circuit will be \(.........\,m \Omega\).

A flexible chain of mass \(m\) hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is \(30^{\circ}\). Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is _________ .

The velocity of upper layer of water in a river is \(36 kmh ^{-1}\). Shearing stress between horizontal layers of water is \(10^{-3} Nm ^{-2}\). Depth of the river is \(m\). (Co-efficiency of viscosity of water is \(10^{-2} \,Pa . s\) )

The graph between two temperature scales \(P\) and \(Q\) is shown in the figure. Between upper fixed point and lower fixed point there are \(150\) equal divisions of scale \(P\) and \(100\) divisions on scale \(Q\). The relationship for conversion between the two scales is given by :

Three objects \(A, B\) and \(C\) are kept in a straight line on a frictionless horizontal surface. The masses of \({A}, {B}\) and \({C}\) are \({m}, 2\, {m}\) and \(2\, {m}\) respectively. \(A\) moves towards \({B}\) with a speed of \(9\) \({m} / {s}\) and makes an elastic collision with it. Thereafter \(B\) makes a completely inelastic collision with \(C.\) All motions occur along same straight line. The final speed of \(C\) is \(....\,{m} / {s}\)

The radius of \(2^{\text {nd }}\) orbit of \(He ^{+}\)of Bohr's model is \(r _1\) and that of fourth orbit of \(Be ^{3+}\) is represented as \(r _2\). Now the ratio \(\frac{r_2}{r_1}\) is \(x : 1\). The value of \(x\) is .........

\(UV\) light of \(4.13 \mathrm{eV}\) is incident on a photosensitive metal surface having work function \(3.13 \mathrm{eV}\). The maximum kinetic energy of ejected photoelectrons will be _______.

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 _______.