If the equilibrium constant for the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$ is $K$,what is the equilibrium constant of $HI_{(g)} \rightleftharpoons \frac{1}{2} H_{2(g)} + \frac{1}{2} I_{2(g)}$?

$K_1, K_2$ and $K_3$ are the equilibrium constants of the following reactions $(I), (II)$ and $(III)$ respectively.
$(I) \, N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(II) \, 2NO_2 \rightleftharpoons N_2 + 2O_2$
$(III) \, NO_2 \rightleftharpoons \frac{1}{2} N_2 + O_2$
The correct relation from the following is

If the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$ at $720 \ K$ has $K = 48$,then for the reaction $2HI_{(g)} \rightleftharpoons H_{2(g)} + I_{2(g)}$,find its equilibrium constant.

$A$ sample of pure $PCl_{5}$ was introduced into an evacuated vessel at $473 \, K$. After equilibrium was attained,the concentration of $PCl_{5}$ was found to be $0.5 \times 10^{-1} \, mol \, L^{-1}$. If the value of $K_{c}$ is $8.3 \times 10^{-3}$,what are the concentrations of $PCl_{3}$ and $Cl_{2}$ at equilibrium?
$PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)}$

For the equilibrium $N_2 + 3H_2 \rightleftharpoons 2NH_3$,$K_c$ at $1000 \ K$ is $2.37 \times 10^{-3}$. If at equilibrium $[N_2] = 2 \ M$ and $[H_2] = 3 \ M$,the concentration of $NH_3$ is: (in $M$)

Give the equilibrium constant expression for the following reactions:
$(a)$ $Ni_{(s)} + 4CO_{(g)} \rightleftharpoons Ni(CO)_{4_{(g)}}$
$(b)$ $Ag_{2}O_{(s)} + 2HNO_{3_{(aq)}} \rightleftharpoons 2AgNO_{3_{(aq)}} + H_{2}O_{(l)}$