If the equilibrium constant for the reaction $2AB \rightleftharpoons A_2 + B_2$ is $49$,then the equilibrium constant for the reaction $AB \rightleftharpoons \frac{1}{2}A_2 + \frac{1}{2}B_2$ will be:

In the figure shown below,reactant $A$ (represented by square) is in equilibrium with product $B$ (represented by circle). The equilibrium constant 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 $780 \ K$ and $10 \ atm$ pressure,the equilibrium constant for the reaction $2 \ A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$ is $3.52$. At the same temperature and $7.04 \ atm$ pressure,the equilibrium constant for the same reaction is:

$2 NOCl_{(g)} \rightleftharpoons 2 NO_{(g)} + Cl_{2(g)}$
In an experiment,$2.0 \ mol$ of $NOCl$ was placed in a $1 \ L$ flask and the concentration of $NO$ after equilibrium was established,was found to be $0.4 \ mol/L$. The equilibrium constant at $30^{\circ} C$ is $....... \times 10^{-4}$.

At $490\,^{\circ}C$,the equilibrium constant for the synthesis of $HI$ is $50$. The value of $K$ for the dissociation of $HI$ will be: