Time period of simple pendulum on earth's surface is '$$\mathrm{T}$$'. Its time period becomes '$$\mathrm{xT}$$' when taken to a height $$\mathrm{R}$$ (equal to earth's radius) above the earth's surface. Then the value of '$$x$$' will be

Consider a soap film on a rectangular frame of wire of area $$3 \times 3 \mathrm{~cm}^2$$. If the area of the soap film is increased to $$5 \times 5 \mathrm{~cm}^2$$, the work done in the process will be (surface tension of soap solution is $$\left.2.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}\right)$$

In Lyman series, series limit of wavelength is $$\lambda_1$$. The wavelength of first line of Lyman series is $$\lambda_2$$ and in Balmer series, the series limit of wavelength is $$\lambda_3$$. Then the relation between $$\lambda_1$$, $$\lambda_2$$ and $$\lambda_3$$ is

The magnetic moment of a current (I) carrying circular coil of radius '$$r$$' and number of turns '$$n$$' depends on