At what temperature, the root mean square speed of gaseous molecules of a gas is equal to their most probable speed at 300 K ?

The value of the square root of the sum of the squares of the stacking velocity values divided by the quantity of values is the root-mean square (RMS) velocity. The RMS velocity is the speed of a wave travelling along a certain ray path across subsurface strata with various interval velocities.

$$\begin{gathered} \frac{3R{T}_2}{M}=\frac{2R{T}_1}{M} \\ \Rightarrow 3T_2=2T_1 \\ \Rightarrow T_2=(2/3)\left(300\mathrm{K}\right)=200\mathrm{K} \end{gathered}$$