If $\tan ^{-1} x = y$,then . . . . . . .

$A$ particle is released from height $S$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of the Earth and the speed of the particle at that instant are respectively:

The circumference of a circle is measured as $56 \text{ cm}$ with an error of $0.02 \text{ cm}$. The percentage error in its area is

The pair of gases responsible for acid rain are

$A$ proton and an $\alpha$-particle are accelerated through a potential difference of $100 \ V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

The internal energy change in a system that has absorbed $2 \, kcal$ of heat and done $500 \, J$ of work is ........... $J$.