At $298 \mathrm{K}$, the molar equilibrium concentrations of ${\mathrm{Ag}}^{+},{\mathrm{NH}}_3$ and ${\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}$for the equilibrium ${\mathrm{Ag}}_{\left(\mathrm{aq}\right)}^{+}+2{\mathrm{NH}}_{3\left(\mathrm{aq}\right)}\iff {\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_3\right]}_{\left(\mathrm{aq}\right)}^{+}$ were found to be ${10}^{-1},{10}^{-3}$, and ${10}^{-1}$ respectively. The value $\mathrm{Kc}$ is

It is given to find the value $\mathrm{Kc}$. At $298 \mathrm{K}$, the molar equilibrium concentrations of ${\mathrm{Ag}}^{+},{\mathrm{NH}}_3$ and ${\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}$for the equilibrium were found to be ${10}^{-1},{10}^{-3}$, and ${10}^{-1}$ respectively.

${\mathrm{Ag}}_{\left(\mathrm{aq}\right)}^{+}+2{\mathrm{NH}}_{3\left(\mathrm{aq}\right)}\iff {\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_3\right]}_{\left(\mathrm{aq}\right)}^{+}$

 $K_c$= $\frac{{\left[{\mathrm{Ag}}_g{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}}{\left[{\mathrm{Ag}}^{+}\right]{\left[{\mathrm{NH}}_3\right]}^2}$ = $\frac{\left({10}^{-1}\right)}{\left({10}^{-1}\right){\left({10}^3\right)}^2}$ = $\frac{{10}^{-1}}{{10}^{-1}{10}^6}$ = ${10}^{-6}$ 

Hence the correct option is (B) ${10}^{-6}$.