An \(npn\) transistor operates as a common emitter amplifier, with a power gain of \(60\, dB\). The input circuit resistance Is \(100\,\Omega \) and the output load resistance is \(10 \,k\,\Omega \). the common emitter current gain \(\beta \) is

A paramagnetic substance in the form of a cube with sides \(1\, cm\) has a magnetic dipole moment of \(20 \times 10^{-6}\, J/T\) when a magnetic intensity of \(60 \times 10^3\, A/m\) is applied. Its magnetic susceptibility is

The gravitational potential at a point above the surface of earth is \(-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}\) and the acceleration due to gravity at that point is \(6.4 \mathrm{~m} / \mathrm{s}^2\). Assume that the mean radius of earth to be \(6400 \mathrm{~km}\). The height of this point above the earth's surface is _______.

The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is

At some instant, a radioactive sample \(S_1\) having an activity \(5\,\mu Ci\)  has twice the number of nuclei as another sample \(S_2\)  which has an activity of  \(10\,\mu Ci.\)  The halflives of \(S_1\)  and  \(S_2\) are

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should by unbinding the strings to achieve a speed of \(4\,ms ^{-1}\), is\(........cm\). \(\left(\right.\) take \(\left.g=10\,ms ^{-2}\right)\)

Two \(10 \; cm\) long, straight wires, each carrying a current of \(5 \; A\) are kept parallel to each other. If each wire experienced a force of \(10^{-5} \; N\), then separation between the wires is \(\dots \; cm\).

A long solenoid is formed by winding \(70\) turns \(cm ^{-1}\). If \(2.0\,A\) current flows, then the magnetic field produced inside the solenoid is \(.......\times 10^{-4}\,T\) \(\left(\mu_0=4 \pi \times 10^{-7}\,TmA ^{-1}\right)\)

If e is the electronic charge, \(c\) is the speed of light in free space and \(h\) is Planck's constant, the quantity \(\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}\) has dimensions of .......

A coaxial cable consists of an inner wire of radius \('a'\) surrounded by an outer shell of inner and outer radii ' \({b}\) ' and '\(c\)' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \({x}\) from the axis when \((i)\) \({x}<{a}\) and \((ii)\) \({a}<{x}<{b}\) ?