When the rms velocity of a gas is denoted by $V$,which of the following relations is true? ($T=$ absolute temperature of the gas)

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $O_2$,vessel $B$ contains only $N_2$,and vessel $C$ contains a mixture of equal quantities of $O_2$ and $N_2$. If the rms speed of $O_2$ molecules in vessel $A$ is $v_1$ and that of $N_2$ molecules in vessel $B$ is $v_2$,then the rms speed of $O_2$ molecules in vessel $C$ is:

At a given temperature,the root mean square velocities of oxygen and hydrogen molecules are in the ratio:

The temperature at which the r.m.s. velocity of hydrogen molecules is $4.5$ times that of an oxygen molecule at $47^{\circ}C$ is (molecular weights of hydrogen and oxygen are $2$ and $32$ respectively). (in $^{\circ}C$)

At $27\,^oC$,the $rms$ velocity of $H_2$ gas is $100\, m/s$. Find the $rms$ velocity of $O_2$ gas at $327\,^oC$.

Out of hydrogen and air,which will have a higher root mean square speed $(v_{\text{rms}})$?