If two planets have their radii in the ratio $$x: y$$ and densities in the ratio $$m: n$$, then the acceleration due to gravity on them are in the ratio

An excited hydrogen atom emits a photon of wavelength $$\lambda$$ in returning to ground state. The quantum number $$n$$ of the excited state is ($$R=$$ Rydberg's constant)

There is hole of area $$A$$ at the bottom of a cylindrical vessel. Water is filled to a height $$h$$ and water flows out in $$t$$ second. If water is filled to a height $$4 h$$, it will flow out in time (in second)

The number of turns in the primary and the secondary of a transformer are 1000 and 3000 , respectively. If $$80 \mathrm{~V} \mathrm{~AC}$$ is applied to the primary coil of the transformer, then the potential difference per turn of the secondary coil would be