On which factors does the velocity distribution of gas molecules depend?

At $T(K)$,the root mean square (rms) velocity of argon (molar mass $40 \ g \ mol^{-1}$) is $20 \ ms^{-1}$. The average kinetic energy of the same gas at $T(K)$ (in $J \ mol^{-1}$) is:

At what temperature will the $RMS$ velocity of $SO_2$ be the same as that of $O_2$ at $303 \ K$?

If the value of $u_{rms}$ at $27\,^{\circ}C$ is $30\sqrt{R}$,what is the molar mass of the gas in kilograms?

The ratio of root mean square velocity of $H_2$ at $50 \ K$ to that of $O_2$ at $800 \ K$ is

Molecular velocities of two gases at the same temperature $(T)$ are $u_{1}$ and $u_{2}$. Their masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expressions is correct at temperature $T$?