Answer
(C) $0.7572$
Work Step by Step
We use Dalton's law to calculate the total pressure
$P_total=P_{H_2}+P_{N_2}+P_{Ar}$
We plug in the known values to obtain:
$P_{total}=0.01887+0.3105+1.027=1.35637atm$
Now, we can calculate the mole fraction of $Ar$
$Mole \space fraction\space of Ar=\frac{P_{Ar}}{P_{total}}$
We plug in the known values to obtain:
$Mole\space fraction \space of Ar=\frac{1.027atm}{1.35637atm}=0.7572$
Thus, option $C$ is correct.