The equivalent resistance between \(A\) and \(B\) is _______.

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively \(\left( k _{\text {sph }}: k _{ cyl }\right)\) is \(2: \sqrt{ x }\), then value of \(x\) is .............

A monoatomic gas having \(\gamma=\frac{5}{3}\) is stored in a thermally insulated container and the gas is suddenly compressed to \(\left(\frac{1}{8}\right)^{\text {th }}\) of its initial volume. The ratio of final pressure and initial pressure is: ( \(\gamma\) is the ratio of specific heats of the gas at constant pressure and at constant volume)

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

A solid sphere of mass \(1\,kg\) rolls without slipping on a plane surface. Its kinetic energy is \(7 \times 10^{-3}\,J\). The speed of the centre of mass of the sphere is \(.........cm s ^{-1}\).

A \(12.5\, eV\) electron beam is used to bombard gaseous hydrogen at room temperature. It will emit

A travelling microscope has \(20\) divisions per \(cm\) on the main scale while its Vernier scale has total \(50\) divisions and \(25\) Vernier scale divisions are equal to \(24\) main scale divisions, what is the least count of the travelling microscope \(..........\,cm\)

In the figure, given that \(V_{BB}\) supply can vary from \(0\) to \(5.0 \,V,\,\,V_{CC} = 5\,V,\) \(\beta _{dc} = 200,\,\,R_B = 100,\,k\Omega ,\) \(R_C = 1\,k\Omega  \) an \(V_{BE} = 1.0\,V,\) The minimum base current and the input voltage at which the transistor will go to saturation, will be respectively

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field \( \vec{E} \) is applied, the final tension in the string changes.The final tension in the string, when pendulum attains an equilibrium position is __________ .
(g: acceleration due to gravity)

Which one is the correct option for the two different thermodynamic processes ?

A submarine experiences a pressure of \(5.05\times 10^6\,Pa\) at a depth of \(d_1\) in a sea. When it goes further to a depth of \(d_2,\) it experiences a pressure of \(8.08\times 10^6\,Pa.\) Then \(d_2 -d_1\) is approximately ........ \(m\) (density of water \(= 10^3\,kg/m^3\) and acceleration due to gravity \(= 10\,ms^{-2}\) )