$\alpha, v$ 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:

Which of the following statement$(s)$ is (are) correct regarding the root mean square speed $(U_{rms})$ and average translational kinetic energy $(\varepsilon_{av})$ of a molecule in a gas at equilibrium?
$(1)$ $U_{rms}$ is doubled when its temperature is increased four times
$(2)$ $\varepsilon_{av}$ at a given temperature does not depend on its molecular mass
$(3)$ $U_{rms}$ is inversely proportional to the square root of its molecular mass
$(4)$ $\varepsilon_{av}$ is doubled when its temperature is increased four times

The $rms$ velocity of a gas depends upon

At what temperature will the $RMS$ velocity of $SO_2$ be the same as that of $O_2$ at $303 \ K$?

Initially,the root mean square $(rms)$ velocity of $N_2$ molecules at a certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms,then the new $rms$ velocity will be:

If the $u_{rms}$ value of a gas at $27\,^oC$ is $30\,R^{1/2}$,then the molar mass of the gas is ........... $kg/mol$.