A) \[{{\left( {{V}_{rms}} \right)}_{1}}<{{\left( {{V}_{rms}} \right)}_{2}}<{{\left( {{V}_{rms}} \right)}_{3}}\And {{\left( \overline{K} \right)}_{1}}={{\left( \overline{K} \right)}_{2}}={{\left( \overline{K} \right)}_{3}}\]
B) \[{{\left( {{V}_{rms}} \right)}_{1}}={{\left( {{V}_{rms}} \right)}_{2}}={{\left( {{V}_{rms}} \right)}_{3}}\And {{\left( \overline{K} \right)}_{1}}={{\left( \overline{K} \right)}_{2}}>{{\left( \overline{K} \right)}_{3}}\]
C) \[{{\left( {{V}_{rms}} \right)}_{1}}>{{\left( {{V}_{rms}} \right)}_{2}}>{{\left( {{V}_{rms}} \right)}_{3}}\And {{\left( \overline{K} \right)}_{1}}<{{\left( \overline{K} \right)}_{2}}>{{\left( \overline{K} \right)}_{3}}\]
D) \[{{\left( {{V}_{rms}} \right)}_{1}}>{{\left( {{V}_{rms}} \right)}_{2}}>{{\left( {{V}_{rms}} \right)}_{3}}\And {{\left( \overline{K} \right)}_{1}}<{{\left( \overline{K} \right)}_{2}}<{{\left( \overline{K} \right)}_{3}}\]
Correct Answer: A
Solution :
[a] \[{{V}_{rms}}\propto \frac{1}{\sqrt{M}}\Rightarrow \left( {{V}_{rms}} \right)<{{\left( {{V}_{rms}} \right)}_{2}}<{{\left( {{V}_{rms}} \right)}_{3}}\] also in mixture temperature of each gas will be same, hence kinetic energy also remains same.
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