When a coil is connected across a \(20 \mathrm{~V}\) DC supply, it draws a current of \(5 \mathrm{~A}\). When it is connected across \(20 \mathrm{~V}, 50 \mathrm{~Hz}\) AC supply, it draws a current of \(4 \mathrm{~A}\). The self inductance of the coil is _______ \(\mathrm{mH}\). (Take \(\pi=3\) )

The number of air molecules per \(\mathrm{cm}^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is \(.........\)

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

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is \(20 cm / s\). The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ \(cm / s\).

Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a} \sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

A poly-atomic molecule ( \(C_V=3 R, C_P=4 R\), where \(R\) is gas constant) goes from phase space point \(\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.\) \(\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)\). A to B is an adiabatic path and \(B\) to \(C\) is an isothermal path. The net heat absorbed per unit mole by the system is :

If the radius of earth shrinks by \(2 \%\) while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.

Let the vertices \(Q\) and \(R\) of the triangle \(P Q R\) lie on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, Q R=5\) and the coordinates of the point \(P\) be \((0,2,3)\). If the area of the triangle \(P Q R\) is \(\frac{m}{n}\) then :

A convex mirror of radius of curvature \(30 \mathrm{~cm}\) forms an image that is half the size of the object. The object distance is :

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of \(5\) times its mass? (Assume the collision to be head-on elastic collision)

The temperature of an ideal gas is increased from \(200\,K\) to \(800\,K\). If r.m.s. speed of gas at \(200\,K\) is \(v_0\). Then, r.m.s. speed of the gas at \(800\,K\) will be:

If \(\mathrm{z}\) is a complex number, then the number of common roots of the equation \(z^{1985}+z^{100}+1=0\) and \(z^3+2 z^2+2 z+1=0\), is equal to :

Let \([ x ]\) denote greatest integer less than or equal to \(x .\) If for \(n \in N ,\left(1-x+x^{3}\right)^{n}=\sum_{j=0}^{3 n} a_{j} x^{j}\), then \(\sum_{j=0}^{\left[\frac{3 n}{2}\right]} a_{2 j}+4 \sum_{j=0}^{\left[\frac{3 n-1}{2}\right]} a_{2 j+1}\) is equal to