The maximum wavelength of radiation emitted by a star is 289.8 nm . Then intensity of radiation for the star is (Given : Stefan's constant $=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$, Wien's constant, $b=2898 \mu \mathrm{mK}$ )

A lift is tied with thick iron ropes having mass ' $M$ '. The maximum acceleration of the lift is ' $a$ ' $\mathrm{m} / \mathrm{s}^2$ and maximum safe stress is ' S ' $\mathrm{N} / \mathrm{m}^2$. The minimum diameter of the rope is

In Balmer series, wavelength of first line is ' $\lambda_1$ ' and in Brackett series wavelength of first line is ' $\lambda_2$ ' then $\frac{\lambda_1}{\lambda_2}$ is

An alternating voltage is given by $E=100 \sin \left(\omega+\frac{\pi}{6}\right) \mathrm{V}$. The voltage will be maximum for the first time when is [ $T=$ periodic time)