A light beam of wavelength \(500\, {nm}\) is incident on a metal having work function of \(1.25\, {eV}\), placed in a magnetic field of intensity \(B\). The electrons emitted perpendicular to the magnetic field \(B\), with maximum kinetic energy are bent into circular arc of radius \(30\, {cm}\). The value of \(B\) is \(....\,\times 10^{-7} \,{T}\). Given \({hc}=20 \times 10^{-26}\, {J}-{m}\), mass of electron \(=9 \times 10^{-31} \,{kg}\)

Given below are two statements : Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be \(0^{\circ}\). Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well : In the light of above statement, choose the correct answer from the options given below.

The diffraction pattern of a light of wavelength \(400\) \(\mathrm{nm}\) diffracting from a slit of width \(0.2 \mathrm{~mm}\) is focused on the focal plane of a convex lens of focal length \(100 \mathrm{~cm}\). The width of the \(1^{\text {st }}\) secondary maxima will be _______.

The ratio of the power of a light source \(S_1\) to that the light source \(S_2\) is \(2 . S_1\) is emitting \(2 \times 10^{15}\) photons per second at 600 nm . If the wavelength of the source \(S_2\) is 300 nm , then the number of photons per second emitted by \(S_2\) is _______ \(\times 10^{14}\).

A singly ionized magnesium atom \((A=24)\) ion is accelerated to kinetic energy \(5\,keV\) and is projected perpendicularly into a magnetic field \(B\) of the magnitude \(0.5\,T\). The radius of path formed will be___________ \(cm\)

The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\)

The dimension of mutual inductance is ............

If the potential barrier across a \(p - n\) junction is \(0.6\,V\). Then the electric field intensity, in the depletion region having the width of \(6 \times 10^{-6} m\), will be \(......\times 10^{5} N / C\).

A \(30\) cm long solenoid has \(10\) turns per cm and area of \(5\) cm\(^2\). The current through the solenoid coil varies from \(2\) A to \(4\) A in \(3.14\) s. The e.m.f. induced in the coil is \(\alpha\times 10^{-5}\) V. The value \(\alpha\) is ________.

The equation of the plane containing the line \(2x- 5y+ z = 3;  x +y+ 4z = 5,\) and parallel to the plane, \(x + 3y+ 6z = 1,\) is:

The energy required to ionise a hydrogen like ion in its ground state is \(9\) Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?  ........\(nm\)

Angular momentum of a single particle moving with constant speed along circular path:

An electromagnetic wave of frequency \(3\, GHz\) enters a dielectric medium of relative electric permittivity \(2.25\) from vacuum. The wavelength of this wave in that medium will be \(.......\,\times 10^{-2} \, cm\)