Which among the following is correct when energy of activation,$E_a$ of the catalyzed reaction decreases at constant temperature and for same concentration?

For a first order reaction,the rate constant is $0.04 \, \text{min}^{-1}$ at $27 \, ^\circ\text{C}$ and $0.08 \, \text{min}^{-1}$ at $37 \, ^\circ\text{C}.$ The activation energy of reaction is .......... $\text{kcal} / \text{mol}$ $(\ln \, 2 = 0.7)$

Which statement is true with respect to a catalyst?

The half-life periods of a first order reaction at $300 \ K$ and $400 \ K$ are $50 \ s$ and $10 \ s$ respectively. The activation energy of the reaction in $kJ \ mol^{-1}$ is $(\log 5 = 0.70)$

The Arrhenius equation expressing the effect of temperature on the rate constant of a reaction is

Two reactions $R_1$ and $R_2$ have identical pre-exponential factors. Activation energy of $R_1$ exceeds that of $R_2$ by $10 \, kJ \, mol^{-1}.$ If $k_1$ and $k_2$ are rate constants for reactions $R_1$ and $R_2$ respectively at $300 \, K,$ then $\ln (k_2/k_1)$ is equal to :
$(R=8.314 \, J \, mol^{-1} \, K^{-1})$