The kinetic theory of gases breaks down at

The root mean square velocity of a gas molecule of mass $m$ at a given temperature is proportional to

Given: $v_1=3 \mathrm{m} {\mathrm{s}}^{-1}, {\mathrm{v}}_2=4 \mathrm{m} {\mathrm{s}}^{-1}$ and $v_3=5 \mathrm{m} {\mathrm{s}}^{-1}$.  What is mean square velocity?

If velocities of three molecules of gas are $3 \mathrm{m} {\mathrm{s}}^{-1}, 4 \mathrm{m} {\mathrm{s}}^{-1}$ and $5 \mathrm{m} {\mathrm{s}}^{-1}$ Then What is the average velocity of gas ?

If velocities of $3$ molecules are $5 \mathrm{m} {\mathrm{s}}^{-1}, 6 \mathrm{m} {\mathrm{s}}^{-1}$ and $7 \mathrm{m} {\mathrm{s}}^{-1}$ respectively, then their mean square velocity in ${\mathrm{m}}^2 {\mathrm{s}}^{-2}$ is

Two molecules have velocities equal to $+5 \mathrm{cm} {\mathrm{s}}^{-1}$ and $-5 \mathrm{cm} {\mathrm{s}}^{-1}$. Their average and root mean square velocities respectively are

Velocities of three molecules are $2, 3$ and $4 \mathrm{m} {\mathrm{s}}^{-1}$ Ratio of mean velocity to $\mathrm{R.M.S.}$ velocity is

Five molecules of gas have velocities $10, 20, 30, 40$ and $50 \mathrm{m} {\mathrm{s}}^{-1}$. The ratio of R.M.S. speed to average speed is

For two gases $A \&\hspace{0.17em}B$ ,$\frac{T_A}{M_A}=4\frac{T_B}{M_B}$ . Here $T$ is the temperature and $M$ is molecular mass.If $V_{RMS}$ is the root-mean-square speed then $\frac{{\left(V_{RMS}\right)}_A}{{\left(V_{RMS}\right)}_B}$ is