$A$ catalyst:

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?

Which one of the following given graphs represents the variation of rate constant $(k)$ with temperature $(T)$ for an endothermic reaction?

For the reaction $A + B \rightarrow C + D$,$\Delta H = -20 \ kJ \ mol^{-1}$. The activation energy for the forward reaction is $85 \ kJ \ mol^{-1}$. The activation energy for the reverse reaction is ......... $kJ \ mol^{-1}$.

For reaction $A \rightarrow P$, rate constant $k = 1.5 \times 10^3 \text{ s}^{-1}$ at $27^\circ\text{C}$. If activation energy for the above reaction is $60 \text{ kJ mol}^{-1}$, then the temperature (in $^\circ\text{C}$) at which rate constant $k = 4.5 \times 10^3 \text{ s}^{-1}$ is . . . . . . .

Write the Arrhenius equation in the form $\ln \, k = -\frac{E_a}{RT} + \ln \, A$.