If a gas is compressed isothermally, then the r.m.s. velocity of the molecules

At what temperature will the oxygen molecules have the same root mean square speed as hydrogen molecules at $200 \, K$ (in $, K$)?

The r.m.s. speed of the molecules of a gas at $100^{\circ} C$ is $v$. The temperature at which the r.m.s. speed will be $\sqrt{3} v$ is: (in $^{\circ} C$)

If the rms velocity of a perfect gas at $27^{\circ} C$ is $500 \,m \cdot s^{-1}$,the same at $927^{\circ} C$ will be

At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

At a temperature of $300 \ K$,the kinetic energy of $O_2$ is $6.21 \times 10^{-21} \ J$ and its $rms$ speed is $484 \ m/s$. What will be the kinetic energy and $rms$ speed at $600 \ K$?