A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are): the average energy per mole of the gas mixture is 2RT; the ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2; the ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/√2; the ratio of speed of sound in the gas mixture to that in helium gas is √6/5.

Checking option A
Average K.E. for 1 mole for mono atomic molecule is given as 3/2RT
Average K.E. for 1 mole for diatomic molecule is given as 5/2RT
Taking average K.E.
K.E.average = (n1K.E.He + n2K.E.H2)/(n1 + n2)
Average K.E. = (3/2RT + 5/2RT)/2 = 2RT
Option A is correct
Checking option B
The velocity of sound in gas is given as V = √(γRT/M)
where γ is ratio of heat capacities, and M is Molecular mass of gas
γaverage = (n1γHe + n2γH2)/(n1 + n2) = (1.6 + 1.4)/2 = 1.5
Maverage = (n1MHe + n2MH2)/(n1 + n2) = (4 + 2)/2 = 3
Checking option C
The R.M.S. speed is given as √(3RT/M)
R.M.S.speed α 1/√M
R.M.S.He/R.M.S.H2 = √(MH2/MHe) = √(2/4) = 1/√2
Hence option C is incorrect and option D is correct
Correct options are A, B and D.