A point object kept at P in front of a glass sphere of radius ' $R$ ' has its image formed at $Q$ such that $\mathrm{PO}=\mathrm{QO}$. The refractive index of material of glass sphere is 1.4. The distance PO is equal to

The magnetic flux through a coil of resistance ' $R$ ' changes by an amount ' $\Delta \phi$ ' in time ' $\Delta t$ '. The amount of induced current and induced charge in the coil are respectively

A circular disc of radius ' $R$ ' and thickness $\frac{R}{8}$ has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere then moment of inertia of sphere about an axis passing through diameter is

When the two known resistance ' $R$ ' and ' $S$ ' are connected in the left and right gaps of a meter bridge respectively, the null point is found at a distance ' $l_1$ ' from the zero end of a meter bridge wire. An unknown resistance ' X ' is now connected in parallel with ' S ' and null point is found at a distance ' $l_2$ ' form zero end of meter bridge wire. The unknown resistance ' X ' is