Correct Answer – C
Root mean square velocity `(V_(rms))=sqrt(3RT)/(M)`
Average velocity `(V_(av))=sqrt(8RT)/(piM)`
For a gas at temperature T, M is constant.
`:.V_(rms)/V_(av)=sqrt(3Rt)/(M)xxsqrt(piM)/(8RT)`
`(sqrt(3)xxsqrt(pi))/(sqrt(8))=(sqrt(3)xxsqrt(3.14))/(sqrt(8))=1.086/1`

Correct Answer – D
According to the kinetic molecular theory of gases , we have
`u_(rms) : u_(aV) = sqrt((3RT)/(M)) : sqrt((8RT)/(pi M))`
`= sqrt(3) : sqrt((8)/(pi))`
` = sqrt(3) : sqrt(2.54)`
`= 1.732 : 1.595`
` = (1.732)/(1.595) : (1.595)/(1.595)`
` = 1.086 : 1`

`v_(rms)=sqrt((3RT)/(M))`
`v_(“average”)=sqrt((8RT)/(piM))`
`(v_(rms))/(v_(“average”))=sqrt((3)/(8pi))=1.086`

Correct Answer – A