The average force applied on the wall of a closed container depends as $\mathrm{T}^{\mathrm{x}}$ where T is the temperature of an ideal gas. The value of $x$ is

Four electric charges $+\mathrm{q},+\mathrm{q},-\mathrm{q}$ and -q are placed in order at the corners of a square of side 2 L. The electric potential at point midway between the two positive charges is

Electron of mass ' $m$ ' and charge ' $q$ ' is travelling with speed ' $v$ ' along a circular path of radius ' $R$ ' at right angles to a uniform magnetic field of intensity ' B '. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

Two coils have a mutual inductance 0.003 H . The current changes in the first coil according to equation $I=I_0 \sin \omega t$, where $I_0=8 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} \mathrm{s}^{-1}$. The maximum value of e.m.f. in the second coil is