What is the role of a catalyst in a chemical reaction?

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

For a first-order reaction at $300 \, ^\circ C$,the activation energy is $35 \, kcal \, mol^{-1}$ and the frequency factor is $1.45 \times 10^{11} \, s^{-1}$. Calculate the rate constant.

The rate constant of a reaction at $25\,^oC$ is $1 \times 10^{-3}\,s^{-1}$. If the rate of the reaction doubles when the temperature is increased to $35\,^oC$,the activation energy of the reaction is .......... $kJ\, mol^{-1}$.

For a first order reaction,the rate of reaction is $2.4 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$ at $27 \ ^\circ C$. The activation energy of the reaction is $24.942 \ kJ \ mol^{-1}$. The rate of reaction at $327 \ ^\circ C$ is ....... $mol \ L^{-1} \ s^{-1}$ [Take $e^5 = 150$,$e^{0.005} = 1$,$e^4 = 55$].

For a chemical reaction,the rate of reaction doubles when the temperature increases by $10\,^oC$. If the temperature is increased from $10\,^oC$ to $100\,^oC$,the rate of reaction will increase by a factor of .....