At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $\,K$)?

The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} C$ in a vessel is $61 \ m/s$. The molecular weight of the gas is nearly:
$[R = 8.31 \ J \ mol^{-1} \ K^{-1}]$

At what temperature is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at $47^{\circ}C$ (in $; K$)?

The root mean square speed of the molecules of a gas is

The relation between root mean square speed $(v_{rms})$ and most probable speed $(v_{p})$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300\, K$ is:

The gas having an average speed four times that of $SO_2$ (molecular mass $64$) is