A) \[{{\left( \frac{{{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....} \right)}^{1/2}}\]
B) \[\frac{{{({{n}_{1}}C_{1}^{2}+{{n}_{2}}C_{2}^{2}+{{n}_{3}}C_{3}^{2}+.....)}^{1/2}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+.....}\]
C) \[\frac{{{({{n}_{1}}C_{1}^{2})}^{1/2}}}{{{n}_{1}}}+\frac{{{({{n}_{2}}C_{2}^{2})}^{1/2}}}{{{n}_{2}}}+\frac{{{({{n}_{3}}C_{3}^{2})}^{1/2}}}{{{n}_{3}}}+......\]
D) \[{{\left[ \frac{{{({{n}_{1}}{{C}_{1}}+{{n}_{2}}{{C}_{2}}+{{n}_{3}}{{C}_{3}}+....)}^{2}}}{({{n}_{1}}+{{n}_{2}}+{{n}_{3}}+....)} \right]}^{1/2}}\]
Correct Answer: A
Solution :
Root mean square speed\[={{\left[ \frac{{{n}_{1}}c_{1}^{2}+{{n}_{2}}c_{2}^{2}+{{n}_{3}}c_{3}^{2}+....}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}+......} \right]}^{1/2}}\].
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