At steady state the charge on the capacitor, as shown in the circuit below, is _________ \(\mu \mathrm{C}\).

An infinite number of point charges, each carrying \(1 \,\mu C\) charge, are placed along the y-axis at \(y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots\) The total force on a \(1 \,C\) point charge, placed at the origin, is \(x \times 10^{3}\, N\). The value of \(x\), to the nearest integer, is ......... [Take \(\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]\)

A galvanometer having coil resistance \(10 \ \Omega\) shows a full scale deflection for a current of \(3 \mathrm{~mA}\). For it to measure a current of \(8 \mathrm{~A}\), the value of the shunt should be:

A particle starts from origin at \(t=0\) with a velocity \(5 \hat{i} \mathrm{~m} / \mathrm{s}\) and moves in \(x-y\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2\). If the \(x\)-coordinate of the particle at that instant is \(84 \mathrm{~m}\), then the speed of the particle at this time is \(\sqrt{\alpha} \mathrm{m} / \mathrm{s}\). The value of \(\alpha\) is___________.

Two planets \(A\) and \(B\) having masses \(m_1\) and \(m_2\) move around the sun in circular orbits of \(r_1\) and \(r_2\) radii respectively. If angular momentum of \(\mathrm{A}\) is \(\mathrm{L}\) and that of \(B\) is \(3L\), the ratio of time period \(\left(\frac{T_A}{T_B}\right)\) is _______.

In photoelectric experiment energy of \(2.48 \mathrm{eV}\) irradiates a photo sensitive material. The stopping potential was measured to be \(0.5 \mathrm{~V}\). Work function of the photo sensitive material is _______.

The intensity of the light from a bulb incident on a surface is \(0.22 \,W / m ^{2}\). The amplitude of the magnetic field in this light-wave is_______ \(\times 10^{-9} \,T\). (Given : Permittivity of vacuum \(\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \,ms ^{-1}\) )

In the figure, potential difference between \(A\) and \(B\) is......\(V\)

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be \(....m\) Given, the length of the rod is \(10 \sqrt{3} m\).

The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______.

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ' is :
( C is the center of curvature of the spherical surface and \(R\) is the radius of curvature)

A ray of light is incident at an angle of \(60^o\) on one face of a prism of angle \(30^o\) . The emergent ray of light makes an angle of \(30^o\)  with incident ray. The angle made by the emergent ray with second face of prism will be....\(^o\)

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then: