Consider an endothermic reaction $X \to Y$ with the activation energies $E_b$ and $E_f$ for the backward and forward reactions,respectively. In general:

$A$ sample of milk splits after $60 \; min.$ at $300 \; K$ and after $40 \; min.$ at $400 \; K$ when the population of $Lactobacillus \; acidophilus$ in it doubles. The activation energy (in $kJ / mol$) for this process is closest to ............. $kJ / mol$.
(Given: $R = 8.3 \; J \; mol^{-1} \; K^{-1}$,$\ln(1.5) = 0.405$)

Find the correct equation among the following.

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 $(A_2 + B_2 \to 2AB)$ in the presence of catalyst will be (in $kJ \ mol^{-1}$)

According to the Arrhenius equation,which of the following statements are correct?
$(A)$ $A$ high activation energy usually implies a fast reaction.
$(B)$ Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
$(C)$ Higher the magnitude of activation energy,stronger is the temperature dependence of the rate constant.
$(D)$ The pre-exponential factor is a measure of the rate at which collisions occur,irrespective of their energy.

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