$A$ gas cylinder can withstand a pressure of $15 \, atm$. The pressure in the cylinder is $12 \, atm$ at $27 \, ^oC$. Up to what temperature in $^oC$ will the cylinder not burst?

The ratio of minimum wavelengths of Lyman and Balmer series will be

$A$ person in an elevator accelerating upwards with an acceleration of $2\,m s^{-2}$ tosses a coin vertically upwards with a speed of $20\,m s^{-1}$. After how much time will the coin fall back into his hand? $(g = 10\,m s^{-2})$

The equations of motion of a projectile are given by $x = 36 t$ metre and $2 y = 96 t - 9.8 t^2$ metre. The angle of projection is:

If $x = \log_{5}(1000)$ and $y = \log_{7}(2058)$,then:

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is (in $, RT$)