If the value of $u_{rms}$ at $27\,^{\circ}C$ is $30\sqrt{R}$,what is the molar mass of the gas in kilograms?

At $133.33 \ K$,the $RMS$ velocity of an ideal gas is $(M = 0.083 \ kg \ mol^{-1}; R = 8.3 \ J \ mol^{-1} \ K^{-1})$ (in $m \ s^{-1}$)

$\alpha, v$ and $u$ represent the most probable velocity, average velocity, and root mean square velocity, respectively, of a gas at a particular temperature. The correct order among the following is:

The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at $300 \ K$ is (Atomic masses: $He = 4 \ u$,$O = 16 \ u$) (in $K$)

The average velocity of ideal gas molecules at $27\,^oC$ is $0.3\,m/s$. The average velocity at $927\,^oC$ is .......... $m/s$.

The temperature of $O_2$ gas at which its $r.m.s.$ speed is equal to the most probable speed of $H_2$ gas at $300 \ K$ is ............... $K$.