Equivalent resistance between the adjacent corners of a regular \(n\)-sided polygon of uniform wire of resistance \(R\) would be:

In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is

In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at \(10.2 \mathrm{~V}\). The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _______ \(\mathrm{nm}\). \(\left(\right.\) Given \(\mathrm{hc}=1245 \mathrm{eV} \mathrm{nm}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) ).

The specific heat at constant pressure of a real gas obeying \(\mathrm{PV}^2=\mathrm{RT}\) equation is _______.

In an experiment with sonometer when a mass of \(180\,g\) is attached to the string, it vibrates with fundamental frequency of \(30\,Hz\). When a mass \(m\) is attached, the string vibrates with fundamental frequency of \(50\,Hz\). The value of \(m\) is \(.........\,g\).

Two circular coils \(P\) and \(Q\)of \(100\) turns each have same radius of \(\pi \mathrm{cm}\). The currents in \(\mathrm{P}\) and \(\mathrm{R}\) are \(1 \mathrm{~A}\) and \(2 \mathrm{~A}\) respectively. \(\mathrm{P}\) and \(\mathrm{Q}\) are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is \(\sqrt{\mathrm{x}} \mathrm{mT}\), where \(\mathrm{x}=\) _______. \(\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\)

A certain gas is isothermally compressed to \(\left(\dfrac{1}{3}\right)^{rd}\) of its initial volume (\(V_o = 3\) litre) by applying required pressure. If the bulk modulus of the gas is \(3 \times 10^5\) N/m\(^2\), the magnitude of work done on the gas is _______ J.

Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by \(\frac{ x }{256} Mr ^2\). The value of x is ___________.

An alternating voltage \(\mathrm{V}(\mathrm{t})=220 \sin 100 \ \pi \mathrm{t}\) volt is applied to a purely resistive load of \(50\ \Omega\). The time taken for the current to rise from half of the peak value to the peak value is _______.