The most probable speed of $O_2$ molecules at $T \ K$ is

The rms velocity $u_{rms}$,mean velocity $u_{av}$ and most probable velocity $u_{mp}$ of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?

If the $V_{rms}$ of a gas is $(30R)^{1/2}$ at $27\,^{\circ}C,$ then calculate the molar mass of the gas in $kg/mol$.

For one mole of a monoatomic gas (molar mass $= M$),the root mean square velocity is $U_{rms}$. What is the relationship between the average kinetic energy $(E)$ and $U_{rms}$?

The average speed of $H_2$ at $T_1 \ K$ is equal to that of $O_2$ at $T_2 \ K$. The ratio $T_1: T_2$ is

By what ratio does the average velocity of a gas molecule change when the temperature is raised from $50^{\circ}C$ to $200^{\circ}C$ (in $: 1$)?