${\mathrm{A}}_{\left(\mathrm{g}\right)},{\mathrm{B}}_{\left(\mathrm{g}\right)}\&{\mathrm{C}}_{\left(\mathrm{g}\right)}$ are present in 1 lit vessel at certain $\mathrm{T}$ under equilibrium at $10 \mathrm{atm}$. If the molar ratio of $\mathrm{A},\mathrm{B}$ to $\mathrm{C}$ is 1:2:2 at equilibrium. ${\mathrm{K}}_{\mathrm{P}}$ for ${\mathrm{A}}_{\left(\mathrm{g}\right)}+2{ \mathrm{B}}_{\left(\mathrm{g}\right)}\rightleftharpoons {\mathrm{C}}_{\left(\mathrm{g}\right)}$ is

 $A+2B\to C$

1       2           2

$1-x 2(2-x) (2+x)$

Total mole$=(1-x)+2(2-x)+(2+x)$

$=1+x+4-2 x+2+x$

$x=0.1$

$K_p=\frac{\left[C\right]}{\left[B{]}^2\right[A]}\frac{\mathrm{atm}}{{\mathrm{atm}}^2 \mathrm{atm}}$

$=(2+x)=0.125$

$=x=0.25{ \mathrm{atm}}^{-1}$

Hence the correct answer (B) $0.25{ \mathrm{atm}}^{-1}$.