The speeds of $5$ gas molecules are $2, 3, 4, 5,$ and $6$ units respectively. What is the $rms$ speed of these molecules?

If the r.m.s. velocity of hydrogen molecules is $4$ times that of an oxygen molecule at $47^{\circ} C$,the temperature of the hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are $2$ and $32$ respectively). (in $^{\circ} C$)

The speed of an oxygen molecule in a gas is $u$. If the temperature is doubled and the molecule dissociates into two atoms,the speed will be:

The temperature of an ideal gas is increased from $27^{\circ}C$ to $927^{\circ}C$. The root mean square speed of its molecules becomes:

Two gases $A$ and $B$ are contained in two separate, but otherwise identical containers. Gas $A$ consists of monatomic molecules, each with atomic mass of $4 \ u$, whereas Gas $B$ consists of rigid diatomic molecules, each with atomic mass of $20 \ u$. If gas $A$ is kept at $27^{\circ} C$, at what temperature should gas $B$ be kept so that both have the same rms speed (in $^{\circ} C$)?

Three vessels $A$,$B$,and $C$ contain gases at the same temperature. Vessel $A$ contains $O_2$ gas,vessel $B$ contains $N_2$ gas,and vessel $C$ contains a mixture of $O_2$ and $N_2$ gases. If the average velocity of $O_2$ in vessel $A$ is $V_1$ and the average velocity of $N_2$ in vessel $B$ is $V_2$,what is the average velocity of $O_2$ in vessel $C$?