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 $m \ s^{-1}$)

At what temperature in $^oC$ will the $rms$ speed of $CO_2$ be equal to the $rms$ speed of $CO$ at $STP$?

The root mean square speeds at $STP$ for the gases $H_2, N_2, O_2$ and $HBr$ are in the order

The distribution of molecular velocities of three gases of molar masses $M_1$,$M_2$,and $M_3$ at $T(K)$ are shown below. The correct relation of their molar masses is:

The root mean square velocity of an ideal gas at constant pressure varies with density $(d)$ as:

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