If the kinetic energy of $O_2$ gas is $4.0 \ kJ \ mol^{-1}$,its $RMS$ speed in $cm \ s^{-1}$ is

At $300 \ K$ the average velocity of a gas is $3 \times 10^2 \ cm / s$. The average velocity (in $cm / s$) of it at $1200 \ K$ 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 $K$)

Amongst the following, which should have the highest $rms$ speed at the same temperature?

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