If the half-lives of a first-order reaction at $350 \ K$ and $300 \ K$ are $2 \ s$ and $20 \ s$ respectively,the activation energy of the reaction in $kJ \ mol^{-1}$ is:

Consider the following statements:
$(i)$ Increase in concentration of reactant increases the rate of a zero order reaction
$(ii)$ Rate constant $k$ is equal to $A$ if $E_a = 0$
$(iii)$ Rate constant $k$ is equal to $A$ if $E_a = \infty$
$(iv)$ $\log_e k$ vs $T$ is a straight line
$(v)$ $\log_e k$ vs $1/T$ is a straight line
Which of the following statements are correct?

For the reaction,$A \rightleftharpoons B$,$E_a = 50 \ kJ \ mol^{-1}$ and $\Delta H = -20 \ kJ \ mol^{-1}$. When a catalyst is added,$E_a$ decreases by $10 \ kJ \ mol^{-1}$. What is the $E_a$ for the backward reaction in the presence of the catalyst?

In a laboratory,a biochemical reaction performed outside the human body in the absence of an enzyme proceeds at a rate $10^{-6}$ times slower. If this reaction is performed in the presence of an enzyme,what will be the activation energy of the reaction?

For a chemical reaction,if the temperature is increased from $25\,^{\circ}C$ to $55\,^{\circ}C$,the rate of reaction will change by a factor of (Assume $\mu = 3$).

Slope of the straight line obtained by plotting $\log_{10} k$ against $\frac{1}{T}$ represents which term?