The $rms$ velocity at $NTP$ of the species can be calculated from the expression

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

If the $RMS$ velocity of an ideal gas is $v \ ms^{-1}$ at $127^{\circ} C$,at what temperature its $RMS$ velocity is doubled (in $K$)?

The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $V_{rms}$. The relation between the average kinetic energy $(E)$ and the $V_{rms}$ is

The gas that has the slowest rate of diffusion among $O_2$,$H_2$,$CO_2$ and $CH_4$ is

At what temperature (in $K$) is the $rms$ velocity of $SO_2$ molecules equal to the $rms$ velocity of $O_2$ molecules at $27^{\circ} C$?