$$\alpha$$, $$v$$ and $$u$$ represent most probable velocity, average velocity and root mean square velocity respectively of a gas at a particular temperature. The correct order among the following is

For an ideal gas obeying Maxwell’s speed distribution, three characteristic speeds are defined:

• Most probable speed (mode) $$\alpha = \sqrt{\frac{2RT}{M}}$$
• Average (mean) speed            $$v = \sqrt{\frac{8RT}{\pi M}}$$
• Root-mean-square (r.m.s.) speed  $$u = \sqrt{\frac{3RT}{M}}$$

To compare them at a fixed temperature, look only at the numerical coefficients under the square roots:

$$\sqrt{3} \approx 1.732, \qquad \sqrt{\frac{8}{\pi}} \approx \sqrt{2.546} \approx 1.595, \qquad \sqrt{2} \approx 1.414$$

Thus

$$u \;(\sqrt{3RT/M}) \; \gt \; v \;(\sqrt{8RT/\pi M}) \; \gt \; \alpha \;(\sqrt{2RT/M}).$$

Hence the correct order is $$u \gt v \gt \alpha$$.

Option A which is: $$u > v > \alpha$$