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

A spherical drop of liquid splits into 1000 identical spherical drops. If '$$\mathrm{E}_1$$' is the surface energy of the original drop and '$$\mathrm{E}_2$$' is the total surface energy of the resulting drops, then $$\frac{E_1}{E_2}=\frac{x}{10}$$. Then value of '$$x$$' is

The displacement of two sinusoidal waves is given by the equation

$$\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x}-30 \mathrm{t}) \\ & \mathrm{y}_2=8 \sin (25 \mathrm{x}-40 \mathrm{t}) \end{aligned}$$

then the phase difference between the waves after time $$t=2 \mathrm{~s}$$ and distance $$x=5 \mathrm{~cm}$$ will be