A plane electromagnetic wave with frequency of \(30 {MHz}\) travels in free space. At particular point in space and time, electric field is \(6 {V} / {m}\). The magnetic field at this point will be \({x} \times 10^{-8} {T}\). The value of \({x}\) is ..... .

The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:-

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm . Total magnification obtained with this system for normal adjustment is \((5)^{ k }\). The value of k is _________

A capacitor of capacitance \(\mathrm{C}\) and potential \(\mathrm{V}\) has energy \(E\). It is connected to another capacitor of capacitance \(2 \mathrm{C}\) and potential \(2 \mathrm{~V}\). Then the loss of energy is \(\frac{x}{3} E\), where \(\mathrm{x}\) is _______.

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is \(\sqrt{n}\) cm. The value of n is

A circular conducting coil of radius \(1\, {m}\) is being heated by the change of magnetic field \(\vec {B}\) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is \(2\, \mu\, \Omega\). The magnetic field is slowly switched off such that its magnitude changes in time as \(B=\frac{4}{\pi} \times 10^{-3}\, {T}\left(1-\frac{{t}}{100}\right)\) The energy dissipated by the coil before the magnetic field is switched off completely is \(E=.....\,{m} J.\)

In an experiment, brass and steel wires of length \(1\,m\) each with areas of cross section \(1\,mm^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of \(0.2\,mm\) is [Given, the Young’s Modulus for steel and brass are respectively \(120\times 10^9\,N/m^2\) and \(60\times 10^9\,N/m^2\) ]

When photon of energy \(4.0\; eV\) strikes the surface of a metal \(\mathrm{A}\), the ejected photoelectrons have maximum kinetic energy \(\mathrm{T}_{\mathrm{A}}\; eV\) end de-Broglie wavelength \(\lambda_{\mathrm{A}} .\) The maximum kinetic energy of photoelectrons liberated from another metal \(\mathrm{B}\) by photon of energy \(4.50 \;eV\) is \(\mathrm{T}_{\mathrm{B}}=\left(\mathrm{T}_{\mathrm{A}}-1.5\right)\;eV\). If the de-Broglie wavelength of these photoelectrons \(\lambda_{B}=2 \lambda_{A}\) then the work function of metal \(\mathrm{B}\) is ............. \(eV\)

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at \(30\) cm above the paper. If the radius of curvature of the lens is \(60\) cm then the refractive index of the lens material is \(\dfrac{\alpha}{10}\). The value of \(\alpha\) is _______.

The escape velocity of a body on a planet  \('A'\)  is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet  \('B'\) , whose density is four times and radius is half of the planet  \('A'\), is ................... \(kms ^{-1}\)

One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in figure. The process \(BC\) is adiabatic. The temperatures at \(A, B\) and \(C\) are \(400\ K, 800\ K \) and \(600\ K\) respectively. Choose the correct statement

In a Young's double slit experiment two slits are separated by \(2\, mm\) and the screen is placed one meter away. When a light of wavelength \(500 \,nm\) is used, the fringe separation will be ........ \(mm\)