Which one of the following does not represent the Arrhenius equation?

The first order rate constant $k$ is related to temperature $T$ as $\log \, k = 15.0 - (10^{6} / T)$. Which of the following pairs of values for the Arrhenius factor $A$ and activation energy $E_a$ is correct?

Activation energy is defined as:

Which of the following statements is not true according to the collision theory of reaction rates?

The rate constant of a reaction at temperature $200 \ K$ is $10$ times less than the rate constant at $400 \ K.$ What is the activation energy $({E_a})$ of the reaction ($R = $ gas constant) (in $R$)?

For the decomposition of $N_2O_5,$ the reaction is $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$ with activation energy $E_a.$ If the reaction is written as $N_2O_{5(g)} \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$ with activation energy $E_a',$ what is the relationship between $E_a$ and $E_a'$?