In the given circuit, the equivalent resistance between the terminal \(A\) and \(B\) is \(........\Omega\).

A parallel plate capacitor has charge \(5 \times 10^{-6} \mathrm{C}\). A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is \(4 \times 10^{-6} \mathrm{C}\) then the dielectric constant of the slab is ________.

A planet takes \(200\) days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

Two particles of equal mass \(\mathrm{m}\) have respective initial velocities \(u\hat{i}\) and \(u\left(\frac{\hat{\mathrm{i}}+ \hat{\mathrm{j}}}{2}\right) .\) They collide completely inelastically. The energy lost in the process is

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

For a given gas at \(1\,atm\) pressure, \(rms\) speed of the molecules is \(200\,m/s\) at \(127\,^oC.\) At \(2\,atm\) pressure and at \(227\,^oC,\) the \(rms\) speed of the molecules will be

Which of the following is not a dimensionless quantity?

As shown in the figure, a potentiometer wire of resistance \(20\,\Omega\) and length \(300\,cm\) is connected with resistance box (R.B.) and a standard cell of emf \(4\,V\). For a resistance ' \(R\) ' of resistance box introduced into the circuit, the null point for a cell of \(20\,mV\) is found to be \(60\,cm\). The value of ' \(R\) ' is \(.....\Omega\)