If the equilibrium constant for the reaction $A + 3B \rightleftharpoons 2C$ is $K_1$,then the equilibrium constant $K_2$ for the reaction $2C \rightleftharpoons A + 3B$ should be:

For the reaction $cis-C_2H_2Cl_2 \rightleftharpoons trans-C_2H_2Cl_2$,the equilibrium constant at $500 \ K$ is $0.6$. The equilibrium constant for the reaction $trans-C_2H_2Cl_2 \rightleftharpoons cis-C_2H_2Cl_2$ at the same temperature will be ...............

At $400 \ K$ for the reaction $2NO_{2(g)} \rightleftharpoons N_{2}O_{4(g)}$,the concentration of $NO_{2}$ is $0.710 \ M$ and $N_{2}O_{4}$ is $0.145 \ M$. Find the equilibrium constant $K_{c}$. (in $M^{-1}$)

For the gaseous reactions $(I)$ and $(II)$,the equilibrium constants are $X$ and $Y$,respectively.
$I. \frac{1}{2} N_{2(g)} + O_{2(g)} \rightleftharpoons NO_{2(g)}$
$II. 2 NO_{2(g)} \rightleftharpoons N_2O_{4(g)}$
Using the above reactions,the equilibrium constant $Z$ for the reaction $(III)$ given below is:
$III. N_2O_{4(g)} \rightleftharpoons N_{2(g)} + 2 O_{2(g)}$

$K_1, K_2$ 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

The equilibrium constant $(K_c)$ for the reaction,$CaSO_4 \cdot 5H_2O_{(s)} \rightleftharpoons CaSO_4 \cdot 3H_2O_{(s)} + 2H_2O_{(g)}$ is equal to