The ratio of the root mean square velocity of $H_2$ at $50 \ K$ to that of $O_2$ at $800 \ K$ 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

For $1 \ mol$ of a gas,the average kinetic energy is $E$. Then the root mean square velocity $U_{rms}$ of the gas is:

Let $(C_{rms})_{H_2}$ be the r.m.s. speed of $H_2$ at $150 \ K$. At what temperature will the most probable speed of helium $[(C_{mp})_{He}]$ be half of $(C_{rms})_{H_2}$ (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

Calculate the root mean square $(rms)$ speed of ozone gas in a closed vessel at a temperature of $20 \, ^\circ C$ and a pressure of $82 \, cm \, Hg$.