For the equilibrium $N_2O_4(g) \rightleftharpoons 2NO_2(g)$ in a closed vessel at a constant temperature,if the volume of the reaction vessel is halved,which of the following statements is true regarding the equilibrium constant $K_p$ and the degree of dissociation $(\alpha)$?

For the following reaction,the equilibrium constant $K_{c}$ at $298 \ K$ is $1.6 \times 10^{17}$.
$Fe^{2+}_{(aq)} + S^{2-}_{(aq)} \rightleftharpoons FeS_{(s)}$
When equal volumes of $0.06 \ M \ Fe^{2+}_{(aq)}$ and $0.2 \ M \ S^{2-}_{(aq)}$ solutions are mixed,the equilibrium concentration of $Fe^{2+}_{(aq)}$ is found to be $Y \times 10^{-17} \ M$. The value of $Y$ is. . . . .

Match the items in List-$X$ with List-$Y$ and select the correct option.

List-$X$	List-$Y$
$(A)$ $A_{(g)} \rightleftharpoons B_{(g)} + \text{Heat}$	$(i)$ Equilibrium constant
$(B)$ $r_b/r_f$	$(ii)$ Favored at low temperature
$(C)$ $r_f/r_b$	$(iii)$ [Equilibrium constant]$^{-1}$
$(D)$ $2A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)}$	$(iv)$ $A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
$(E)$ Effect of pressure	$(V)$ $\Delta n < 0$

For the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$,the equilibrium constants $K_p$ and $K_q$ are in the ratio $1:9$. If the degree of dissociation of $X$ and $Z$ is the same,then the ratio of their total pressures is:

Dissociation of a gas $A_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is $1 \ bar$ at $300 \ K$.
$A_{2(g)} \rightleftharpoons 2A_{(g)}$
The standard Gibbs energy of formation of the involved substances has been provided below:

Substance	$\Delta G_f^{\circ} / kJ \ mol^{-1}$
$A_2$	$-100.00$
$A$	$-50.832$

The degree of dissociation of $A_{2(g)}$ is given by $(x \times 10^{-2})^{1/2}$ where $x =$ . . . . . . . (Nearest integer).
[Given: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$, $\ln 2 = 0.693$]

Consider the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$. The equilibrium constant of the above reaction is $K_p$. If pure ammonia is left to dissociate,the partial pressure of ammonia at equilibrium is given by (Assume that $P_{NH_3} \ll P_{total}$ at equilibrium and $P$ is the total pressure).