The density of a gas at $100 \, kPa$ pressure is $0.1 \, g \, cm^{-3}$. What will be its $rms$ speed in $m \, s^{-1}$?

The molecular weight of a gas that diffuses twice as rapidly as the gas with molecular weight $64$ is:

Root mean square $(rms)$ speed of $O_2$ is $500 \ m/s$ at a constant temperature. Calculate the $rms$ speed and the average kinetic energy of $H_2$ at the same temperature. (Consider, $R=8.33 \ J \ K^{-1} \ mol^{-1}$)

The $rms$ speed of hydrogen is $\sqrt{7}$ times the $rms$ speed of nitrogen. If the temperature of the gases is $T$,then:

If the most probable speed of $CO_2$ at $27^{\circ} C$ is $400 \ ms^{-1}$,the root mean square velocity of $CO_2$ at the same temperature in $ms^{-1}$ is approximately:

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