In a certain thermodynamical process, the pressure of a gas depends on its volume as \(kV ^{3}\). The work done when the temperature changes from \(100^{\circ} C\) to \(300^{\circ} C\) will be .......... \(nR\), where \(n\) denotes number of moles of a gas.

\(\left(P+\frac{a}{V^2}\right)(V-b)=R T\) represents the equation of state of some gases. Where \(P\) is the pressure, \(V\) is the volume, \(T\) is the temperature and \(a, b, R\) are the constants. The physical quantity, which has dimensional formula as that of \(\frac{b^2}{a}\), will be

A diode has Zener voltage of \(10\) V and maximum power dissipation of \(0.5\) W, then the minimum resistance to be used in series with this diode for safety when it is connected to a \(25\) V power supply is ______ \(\Omega\).

A straight wire carrying a current of \(14\,A\) is bent into a semicircular are of radius \(2.2\,cm\) as shown in the figure. The magnetic field produced by the current at the centre \((O)\) of the arc. is \(.........\,\times 10^{-4}\, T\)

Three capacitors of capacitances \(25 \mu \mathrm{F}, 30 \mu \mathrm{F}\) and \(45 \mu \mathrm{F}\) are connected in parallel to a supply of \(100\) \(V\). Energy stored in the above combination is \(\mathrm{E}\). When these capacitors are connected in series to the same supply, the stored energy is \(\frac{9}{\mathrm{x}} \mathrm{E}\). The value of \(x\) 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 \(.........\,g\).

A fighter plane of length \(20\, m\), wing span (distance from tip of one wing to the tip of the other wing) of \(15\,m\) and height \(5\,m\) is lying towards east over Delhi. Its speed is \(240\, ms^{-1}\) . The earth's magnetic field over Delhi is \(5 \times 10^{-5}\,T\) with the declination angle \( \sim {0^o}\) and dip of \(\theta\) such that \(\sin \,\theta  = \frac{2}{3}\). If the voltage developed is \(V_B\) between the lower and upper side of the plane and \(V_W\) between the tips of the wings then \(V_B\) and \(V_W\) are close to

Two infinite planes each with uniform surface charge density \(+\sigma\) are kept in such a way that the angle between them is \(30^{\circ} .\) The electric field in the region shown between them is given by

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed \('v'\) in a uniform magnetic field \(B\) going into the plane of the paper (See figure). If charge densities \({\sigma _1}\) and \({\sigma _2}\) are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)

The charge stored by the capacitor C in the given circuit in the steady state is _________ \(\mu C\).