Molecular Speeds — Prelims Questions

At what temperature will the root mean square speed of oxygen molecules ($O_2$) be equal to the root mean square speed of hydrogen molecules ($H_2$) at $27^circ C$?

The ratio of the most probable speed to the average speed of a gas molecule at a given temperature is:

If the temperature of an ideal gas is increased from $T$ to $4T$, what will be the change in its root mean square speed?

Which of the following statements about molecular speeds is INCORRECT?

If the molar mass of a gas is doubled, at constant temperature, how will its root mean square speed change?

A gas mixture contains equal moles of hydrogen ($H_2$) and oxygen ($O_2$). If the temperature of the mixture is $300,\text{K}$, what is the ratio of the average speed of hydrogen to that of oxygen?