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

The ratio of magnetic field at the centre of the current carrying circular loop and magnetic moment is $$X$$. When both the current and radius are doubled, then the ratio will be