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

The ratio between the $RMS$ velocity of $N_2$ at $200 \ K$ and that of $CO$ at $800 \ K$ is (molecular mass of $N_2 = 28 \ g \ mol^{-1}$, molecular mass of $CO = 28 \ g \ mol^{-1}$)

At what temperature in $^oC$ will the $rms$ speed of $CO_2$ be equal to the $rms$ speed of $CO$ at $STP$?

Initially,the root mean square $(rms)$ velocity of $N_2$ molecules at a certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms,then the new $rms$ velocity will be:

The root mean square velocity of a gas molecule is proportional to:

The average speed of a gas molecule is $400 \, m/s$. Calculate its $rms$ speed at the same temperature in $m/s$.