In respect of the equation $k = A e^{-E_a/RT}$ in chemical kinetics,which one of the following statements is correct?

Consider the following reversible reaction,
$A_{(g)} + B_{(g)} \rightleftharpoons AB_{(g)}.$
The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in $J \ mol^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction,the absolute value of $\Delta G^{\ominus}$ (in $J \ mol^{-1}$) for the reaction at $300 \ K$ is. . . . . (Given; $\ln(2)=0.7, RT=2500 \ J \ mol^{-1}$ at $300 \ K$ and $G$ is the Gibbs energy)

For the reaction $X \rightleftharpoons Y$,the pre-exponential factors for the forward and backward reactions are equal. What will be the equilibrium constant of the reaction?

For a reversible reaction $A \rightleftharpoons B$,which one of the following statements is wrong from the given energy profile diagram?

Consider the following plots of rate constant versus $\frac{1}{T}$ for four different reactions. Which of the following orders is correct for the activation energies of these reactions?

At $27^{\circ}C$ in the presence of a catalyst, the activation energy of a reaction is lowered by $10 \ kJ \ mol^{-1}$. The logarithm ratio of $\frac{k(\text{catalysed})}{k(\text{uncatalysed})}$ is .... (Consider that the frequency factor for both the reactions is the same)