The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is

Two point charges $+8 q$ and $-2 q$ are located at $\mathrm{X}=0$ (origin) and $\mathrm{X}=\mathrm{L}$ respectively. The net electric field due to these two charges is zero at point $P$ on $X$-axis. The location of point $P$ from the origin is

A series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit containing a resistance ' $R$ ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $V_R$ ' and ' $\mathrm{V}_{\mathrm{L}}$ ' respectively, then value of capacitance will be

Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gaussian surface is in the form of a cylinder of radius ' $r$ ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder $(r< R)$, electric field is directly proportional to