At what temperature is the root mean square (rms) speed of Neon gas atoms equal to the rms speed of Helium gas atoms at $-33^{\circ} C$ (in $K$)? (Atomic mass of $Ne = 20.2 \ u$ and that of $He = 4.0 \ u$)

The speeds of $5$ molecules of a gas (in arbitrary units) are as follows: $2, 3, 4, 5, 6$. The root mean square speed for these molecules is

In two vessels of the same volume,atomic hydrogen and helium at pressures of $1\, atm$ and $2\, atm$ are filled,respectively. If the temperature of both samples is the same,then the average speed of hydrogen atoms $\langle C_H \rangle$ will be related to that of helium $\langle C_{He} \rangle$ as:

The speeds of ten particles in $ms^{-1}$ are $0, 2, 3, 4, 4, 4, 5, 5, 6, 9$. The values of average speed,$rms$ speed,and most probable speed are respectively:

At what temperature will the root mean square speed $(\nu_{rms})$ of oxygen gas molecules be equal to the $\nu_{rms}$ of hydrogen gas molecules at $27 \, ^\circ C$? $(M_{O_2} = 32 \, g \, mol^{-1}, M_{H_2} = 2 \, g \, mol^{-1})$

The gas having average speed four times as that of $SO_{2}$ (molecular mass $64$) is