Equal volumes of two gases,having their densities in the ratio of $1: 16$,exert equal pressures on the walls of two containers. The ratio of their rms speeds $(c_1: c_2)$ is

The Maxwell distribution function for different gases is shown in the figure. Which of the following is the correct matching?

The temperature of a gas is $-50^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed is increased by $3$ times?

Let $A$ and $B$ be two gases and given: $\frac{T_A}{M_A} = 4 \cdot \frac{T_B}{M_B}$,where $T$ is the temperature and $M$ is the molecular mass. If $C_A$ and $C_B$ are the $r.m.s.$ speeds,then the ratio $\frac{C_A}{C_B}$ will be equal to:

Consider a sample of oxygen behaving like an ideal gas. At $300 \, K$,the ratio of root mean square (rms) velocity to the average velocity of gas molecules would be: (Molecular weight of oxygen is $32 \, g/mol$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$)

Column-$I$ represents the formula for ${v_{rms}}$ and Column-$II$ represents the corresponding condition (phenomena). Match them correctly:

Column-$I$	Column-$II$
$(a)$ ${v_{rms}} = \sqrt {\frac{3P}{\rho}}$	$(i)$ For $1 \text{ mole ideal gas}$
$(b)$ ${v_{rms}} = \sqrt {\frac{3RT}{M_0}}$	$(ii)$ For one molecule of gas
$(c)$ ${v_{rms}} = \sqrt {\frac{3{k_B}T}{m}}$	$(iii)$ On the basis of kinetic theory