What is the role of a catalyst in a chemical reaction?

For a first-order reaction,if the rate constant is $k_1$ at temperature $T_1$ and $k_2$ at temperature $T_2$,which of the following relations is correct? ($E_a$ = activation energy)

The energies of activation for forward and reverse reactions for $A_2 + B_2 \rightleftharpoons 2AB$ are $180 \, kJ \, mol^{-1}$ and $200 \, kJ \, mol^{-1}$ respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by $100 \, kJ \, mol^{-1}.$ The enthalpy change of the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of a catalyst will be (in $kJ \, mol^{-1}$)

For a first-order reaction at $300 \, ^\circ C$,the activation energy is $35 \, kcal \, mol^{-1}$ and the frequency factor is $1.45 \times 10^{11} \, s^{-1}$. Calculate the rate constant.

The following figure shows a graph of $\log_{10}K$ vs $\frac{1}{T}$,where $K$ is the rate constant and $T$ is the temperature. The straight line $BC$ has a slope,$\tan \theta = -\frac{1}{2.303}$,and an intercept of $5$ on the $Y$-axis. Thus,$E_a$,the energy of activation,is ....... $cal$.

Which among the following equations represents the Arrhenius equation?