According to the Arrhenius equation,a plot of the logarithm of the rate constant $(\log \, k)$ versus which of the following yields a straight line?

Activation energy for the acid catalysed hydration of sucrose is $6.22 \ kJ \ mol^{-1}$,while the activation energy is only $2.15 \ kJ \ mol^{-1}$ when hydrolysis is catalysed by the enzyme sucrase. Explain.

According to the collision theory of chemical reactions:

For a reaction $E_a = 0$ and $k = 3.2 \times 10^8 \ s^{-1}$ at $300 \ K$. The value of frequency factor at $400 \ K$ would be

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?

The correct reaction profile diagram for a positive catalyst reaction.