At what temperature (in $K$) is the $rms$ velocity of $SO_2$ molecules equal to the $rms$ velocity of $O_2$ molecules at $27^{\circ} C$?

If the most probable speed of $CO_2$ at $27^{\circ} C$ is $400 \ ms^{-1}$,the root mean square velocity of $CO_2$ at the same temperature in $ms^{-1}$ is approximately:

If the distribution of molecular speeds of a gas is as per the figure shown below,then the ratio of the most probable,the average and the root mean square speeds,respectively,is

The rms velocity of oxygen molecules at $27^{\circ} C$ is around $800 \ m/s$. The rms velocity of methane molecules at $600 \ K$ temperature is around ...... (in $m/s$)

The temperature of an ideal gas increases from $120 \ K$ to $480 \ K$. If the root mean square velocity of the gas molecules at $120 \ K$ is $v$,then at $480 \ K$ it will be .......

The average speed of $CH_4$ molecules at $300 \ K$ is equal to the average speed of $O_2$ molecules at ............ $K$.