The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$x$$ is _________.

A steel rod of length $$1 \mathrm{~m}$$ and cross sectional area $$10^{-4} \mathrm{~m}^{2}$$ is heated from $$0^{\circ} \mathrm{C}$$ to $$200^{\circ} \mathrm{C}$$ without being allowed to extend or bend. The compressive tension produced in the rod is ___________ $$\times 10^{4} \mathrm{~N}$$. (Given Young's modulus of steel $$=2 \times 10^{11} \mathrm{Nm}^{-2}$$, coefficient of linear expansion $$=10^{-5} \mathrm{~K}^{-1}$$ )

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $$3 \mathrm{~m} / \mathrm{s}$$ (as shown in figure). Maximum height with respect to the initial position covered by it will be __________ cm.

The ratio of magnetic field at the centre of a current carrying coil of radius $$r$$ to the magnetic field at distance $$r$$ from the centre of coil on its axis is $$\sqrt{x}: 1$$. The value of $$x$$ is __________