Assertion $(A)$ : $A$ catalyst increases the rate of a reaction.
Reason $(R)$ : In presence of a catalyst, the activation energy of the reaction increases.
The correct answer is

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 $E_a'$?

Correct statements regarding Arrhenius equation among the following are:
$(A)$ Factor $e^{-Ea/RT}$ corresponds to fraction of molecules having kinetic energy less than $Ea$.
$(B)$ At a given temperature, lower the $Ea$, faster is the reaction.
$(C)$ Increase in temperature by about $10^{\circ}C$ doubles the rate of reaction.
$(D)$ Plot of $\log k$ vs $\frac{1}{T}$ gives a straight line with $slope = -\frac{Ea}{2.303R}$.
Choose the correct answer from the options given below:

In a reaction, for every $10^{\circ} C$ rise of temperature, the rate is doubled. If the temperature is increased from $10^{\circ} C$ to $100^{\circ} C$, the rate of the reaction will become $:-$ (in $\times$)

$A$ reaction rate constant is given by $k = 1.2 \times 10^{14} \, e^{-25000/RT} \, sec^{-1}$. It means

What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?