A gas mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes we calculated the total internal energy of the system to be $xRT$. What is the value of $x$?

The internal energy of n moles of a gas is $U=\frac{1}{2}\mathit{\text{nFRT}}$
where F = number of degrees of freedom.
The internal energy of 2 moles of oxygen at temperature T is

${\mathit{\text{U}}}_1=\frac{1}{2}\times 2\times 5\mathit{\text{RT}}=5\mathit{\text{RT}}$    (F = 5 for oxygen molecule)

The total internal energy of 4 moles of argon at temperature T is

    $U_2=\frac{1}{2}\times 4\times 3\mathit{\text{RT}}=6\mathit{\text{RT}}$ (F = 3 for argon molecule)

Total internal energy $=U_1+U_2=11\mathit{\text{RT}}$

$\Rightarrow x=11$