At what temperature is the $rms$ speed of hydrogen molecules equal to the $rms$ speed of oxygen molecules at $47^{\circ}C$ (in $K$)?

Consider a sample of oxygen behaving like an ideal gas. At $300 \, K$,the ratio of root mean square (rms) velocity to the average velocity of gas molecules would be: (Molecular weight of oxygen is $32 \, g/mol$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$)

If the molecular weights of two gases are $M_1$ and $M_2$,then at a constant temperature,the ratio of their root mean square velocities $v_1$ and $v_2$ will be:

If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

The rms speed of an oxygen molecule at a certain temperature is $600 \,ms^{-1}$. If the temperature is doubled and the oxygen molecule dissociates into atomic oxygen atoms,the new rms speed is (in $\,ms^{-1}$)

The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?