Which of the following statements is/are true about equilibrium?

(a) Equilibrium is possible only in a closed system of at a given temperature

(b) All the measurable properties of the system remain constant at equilibrium

(c) Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

According to Le Chatelier's principle, in the reaction $\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$, the formation of methane is favoured by

(a) Increasing the concentration of CO

(b) Increasing the concentration of $\mathrm{H}_2 \mathrm{O}$

(c) Decreasing the concentration of $\mathrm{CH}_4$

(d) Decreasing the concentration of $\mathrm{H}_2$

The equilibrium constant at 298 K for the reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 . If the initial concentrations of all the four species were 1 M each, then equilibrium concentration of D (in $\mathrm{mol} \mathrm{L}^{-1}$ ) will be

At $$500 \mathrm{~K}$$, for a reversible reaction $$A_2(g)+B_2(g) \rightleftharpoons 2 A B(g)$$ in a closed container, $$K_C=2 \times 10^{-5}$$. In the presence of catalyst, the equilibrium is attaining 10 times faster. The equilibrium constant $$K_C$$ in the presence of catalyst at the same temperature is