An electron of a hydrogen like atom, having \(Z=4\), jumps from \(4^{\text {th }}\) energy state to \(2^{\text {nd }}\) energy state, The energy released in this process, will be \(.........eV\) \((\) Given \(Rch =13.6\,eV )\) Where \(R =\) Rydberg constant \(c=\) Speed of light in vacuum \(h =\) Planck's constant

A cubical block of side \(30\,cm\)  is moving with  velocity \(2\,\,ms^{-1}\) on a smooth horizontal surface. The surface has a bump at a point \(O\) as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are :
\(\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2\) and \(\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}\). The free ends of rods A and B are maintained at \(400 \mathrm{~K}, 200 \mathrm{~K}\), respectively. The temperature of rods interface is ________ K, when equilibrium is established.

In an experiment to measure focal length \((f)\) of convex lens, the least counts of the measuring scales for the position of object \((u)\) and for the position of image \((v)\) are \(\Delta u\) and \(\Delta v\), respectively. The error in the measurement of the focal length of the convex lens will be _______.

The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.

A Carnot engine has efficiency of \(50 \%\). If the temperature of sink is reduced by \(40^{\circ} C\), its efficiency increases by \(30 \%\). The temperature of the source will be\(....K\)

Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______.

Consider two ideal diatomic gases \(\mathrm{A}\) and \(\mathrm{B}\) at some temperature \(T\). Molecules of the gas \(A\) are rigid, and have a mass \(m\). Molecules of the gas \(\mathrm{B}\) have an additional vibrational mode, and have a mass \(\frac{\mathrm{m}}{4} .\) The ratio of the specific heats \((\mathrm{C}_{\mathrm{v}}^{\mathrm{A}}\) and \(\mathrm{C}_{\mathrm{v}}^{\mathrm{B}})\) of gas \(\mathrm{A}\) and \(\mathrm{B}\), respectively is

Four identical hollow cylindrical columns of mild steel support a big structure of mass \(50 \times 10^{3} {kg}\), The inner and outer radii of each column are \(50\; {cm}\) and \(100 \;{cm}\) respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use \(\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]\)

A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\)  \((g\, = 10\, m\,s^{-2})\)