Two coils P and Q each of radius R carry currents I and $\sqrt{8} \mathrm{I}$ respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ( $\mu_0=$ permeability of free space)

In Young's double slit experiment, intensity at a point is $\left(\frac{1}{4}\right)$ of the maximum intensity. The angular position of this point is

The mutual inductance of two coils is 45 mH . The self-inductance of the coils are $\mathrm{L}_1=75 \mathrm{mH}$ and $\mathrm{L}_2=48 \mathrm{mH}$. The coefficient of coupling between the two coils is

Frequency of the series limit of Balmer series of hydrogen atom of Rydberg's constant ' $R$ ' and velocity of light ' $C$ ' is