The value of $K_{c}$ for the reaction $2 A \rightleftharpoons B + C$ is $2 \times 10^{-3}$. At a given time,the composition of the reaction mixture is $[ A ] = [ B ] = [ C ] = 3 \times 10^{-4} \ M$. In which direction will the reaction proceed?

For the reaction ${N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$,the equilibrium constant ${K_p = 35}$ at a given temperature. Calculate the values of ${K_p}$ for the following reactions at the same temperature:
$(i) \ 2NH_3(g) \rightleftharpoons N_2(g) + 3H_2(g)$
$(ii) \ \frac{1}{2}N_2(g) + \frac{3}{2}H_2(g) \rightleftharpoons NH_3(g)$

For the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,the correct expression of equilibrium constant $K$ is

$K_1, K_2$ 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

At a definite temperature,the $K_c$ of the following reaction is $0.18$: $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$. In a reaction mixture at the same temperature,$[PCl_3] = 0.042 \ M$,$[Cl_2] = 0.024 \ M$,and $[PCl_5] = 0.005 \ M$. Is this reaction in equilibrium? In which direction will the reaction proceed?

If the equilibrium constant for the reaction,$2 SO_2 + O_2 \rightleftharpoons 2 SO_3$ is $64$ at $500 \ K$,then the equilibrium constant for the reaction $SO_3 \rightleftharpoons SO_2 + \frac{1}{2} O_2$ at the same temperature is