What is the relationship between the temperature $T$ and the activation energy $E_a$ in the Arrhenius equation?

The rate constant of a reaction is increased $4$ times after the addition of a catalyst to the reaction mixture at the same temperature of $27^{\circ} C$. The change in the activation energy of this reaction is (Take $\ln(1/4) = -1.386, R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

The variation of the rate constant with temperature is given by the Arrhenius equation $k = A e^{-E_a / (RT)}$. If $T \to \infty$,the rate constant $k$ will be equal to:

In respect of the equation $k = A e^{-E_a/RT}$ in chemical kinetics,which one of the following statements is correct?

For a reaction $A \rightarrow B$,the enthalpy of reaction is $-4.2 \ kJ \ mol^{-1}$ and the enthalpy of activation is $9.6 \ kJ \ mol^{-1}$. The correct potential energy profile for the reaction is shown in which option?

In the Arrhenius equation,the fraction of molecules having energy equal to or greater than the activation energy at a given temperature is represented by .....