In Young's double slit experiment, the '$$\mathrm{n^{th}}$$' maximum of wavelength '$$\lambda_1$$' is at a distance '$$\mathrm{y_1}$$' from the central maximum. When the wavelength of the source is changed to '$$\lambda_2$$', $$\left(\frac{\mathrm{n}}{2}\right)^{\text {th }}$$ maximum is at a distance of '$$\mathrm{y_2}$$' from its central maximum. The ratio $$\frac{y_1}{y_2}$$ is

A perfectly black body emits a radiation at temperature 'T$$_1$$' K. If it is to radiate at 16 times this power, its temperature 'T$$_2$$' K should be

Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop is

Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant, maximum distance between two particles is $$\sqrt{2}$$ a. The initial phase difference between them is

$$\left[\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4}\right]$$