Thank you for reporting, we will resolve it shortly
Q.
$1$ mole of $HI$ is heated in a closed container of capacity of $2\, L$. At equilibrium half a mole of $HI$ is dissociated. The equilibrium constant of the reaction is
$ K _{ C } \frac{\left[ H _{2}\right]\left[ I _{2}\right]}{[ HI ]^{2}} $
$ K _{ C }= \frac{\frac{0.25 \times 0.25}{2}}{\frac{0.5 \times 0.5}{2}}$
$=\frac{1}{4}=0.25 $