At which temperature will the average velocity of ammonia $(NH_3)$ molecules be identical to the average velocity of nitric oxide $(NO)$ molecules at $327\,^oC$?

The rms velocity $u_{rms}$,mean velocity $u_{av}$ and most probable velocity $u_{mp}$ of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?

The ratio among most probable velocity,mean velocity and root mean square velocity is given by

If the $v_{rms}$ is $30 R^{1/2}$ at $27 ^\circ C$,then calculate the molar mass of the gas in kilograms.

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

What is the kinetic energy (in $J \ mol^{-1}$) of one mole of an ideal gas (molar mass $= 0.1 \ kg \ mol^{-1}$) if its rms velocity is $4 \times 10^2 \ ms^{-1}$ at $T(K)$?