A light ray enters a solid glass sphere of refractive index \(\mu=\sqrt{3}\) at an angle of incidence \(60^{\circ}\). The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is......

For \(LED's\)  to emit light in visible region of electromagnetic light, it should have energy band gap in the range of

For the given circuit, comment on the type of transformer used:

A hydraulic automobile lift is designed to lift vehicles of mass \(5000\,kg\). The area of cross section of the cylinder carrying the load is \(250\,cm ^2\). The maximum pressure the smaller piston would have to bear is [Assume \(g=10\,m / s ^2\)]

A series \(LCR\) circuit is designed to resonate at an angular frequency \(\omega_{0}=10^{5} \,rad / s\). The circuit draws \(16\, W\) power from \(120\, V\) source at resonance. The value of resistance \('R'\) in the circuit is ...... \(\Omega\).

The wavelength of the photon emitted by a hydrogen atom when an electron makes a  transition from \(n =2\) to \(n =1\) state is ...... \(nm.\)

Two identical small bar magnets each of dipole moment \(3\sqrt{5}\) J/T are placed at a center to center separation of \(10\) cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is \(\alpha \times 10^{-3}\) T. The value of \(\alpha\) is ______.
(\(\mu_0=4\pi \times 10^{-7}\) Tm/A)

A vehicle travels \(4\,km\) with speed of \(3\,km / h\) and another \(4\,km\) with speed of \(5\,km / h\), then its average speed is \(..........km/h\)

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

A current of \(1\,A\) is flowing on the sides of an equilateral triangle of side \(4.5\times10^{-2}\,m\) . The magnetic field at the centre of the triangle will be

A tuning fork \(A\) of unknown frequency produces \(5\, beats/s\) with a fork of known frequency \(340\, Hz\). When fork \(A\) is filed, the beat frequency decreases to \(2\, beats/s.\) What is the frequency of fork \(A\) ? (in \(Hz\))

A homogeneous solid cylindrical roller of radius \(R\) and mass \(M\) is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

Two persons pull a wire towards themselves. Each person exerts a force of \(200 \mathrm{~N}\) on the wire. Young's modulus of the material of wire is \(1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Original length of the wire is \(2 \mathrm{~m}\) and the area of cross section is \(2 \mathrm{~cm}^2\). The wire will extend in length by _______ \(\mu \mathrm{m}\).