According to the collision theory of reaction rates:

The rate constant of a first-order reaction is $1.5 \times 10^7 \text{ s}^{-1}$ at $300 \text{ K}$ and $3.0 \times 10^7 \text{ s}^{-1}$ at $330 \text{ K}$. What is the activation energy $(E_a)$ for the reaction? $[R \times 2.303 = 19.15 \text{ J K}^{-1} \text{mol}^{-1}]$

When the temperature changes from $293 \ K$ to $313 \ K$,the rate of a certain reaction becomes four times. Find the activation energy of the reaction in $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

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 a first-order gaseous reaction,a plot of $\log \, k$ versus $1/T$ gives a straight line with a slope of $-8000$. Calculate the activation energy $(E_a)$ of the reaction in $cal$.

According to the collision theory of chemical reaction,which of the following is correct?