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

Case $-1:$ An ideal gas of molecular weight $M$ at temperature $T$.
Case $-2:$ Another ideal gas of molecular weight $2M$ at temperature $T/2$.
Identify the correct statement in the context of the above two cases.

At $300 \ K$ the average velocity of a gas is $3 \times 10^2 \ cm / s$. The average velocity (in $cm / s$) of it at $1200 \ K$ is

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

At room temperature,the average speed of helium is higher than that of oxygen by a factor of

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