The Arrhenius equation is represented as $k = A e^{-E_a/RT}$. The activation energy $E_a$ of the reaction can be calculated by plotting:

How much faster would a reaction proceed at $25\,^{\circ}C$ than at $0\,^{\circ}C$ if the activation energy is $65\,kJ/mol$?

The slope of the graph drawn between $\ln k$ and $\frac{1}{T}$ as per Arrhenius equation gives the value ($R=$ gas constant,$E_a=$ Activation energy)

The number of given statement/s which is/are correct is $.....$.
$(A)$ The stronger the temperature dependence of the rate constant,the higher is the activation energy.
$(B)$ If a reaction has zero activation energy,its rate is independent of temperature.
$(C)$ The stronger the temperature dependence of the rate constant,the smaller is the activation energy.
$(D)$ If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.

For a reversible chemical reaction where the forward process is exothermic,which of the following statements is correct?

For reaction $A \to B$,rate constant $K_1 = A_1 e^{-E_{a_1}/RT}$ and for the reaction $X \to Y$,rate constant $K_2 = A_2 e^{-E_{a_2}/RT}$. If $A_1 = 10^8, A_2 = 10^{10}$ and $E_{a_1} = 600 \ cal \ mol^{-1}$,$E_{a_2} = 1800 \ cal \ mol^{-1}$,then the temperature at which $K_1 = K_2$ is (given: $R = 2 \ cal \ K^{-1} \ mol^{-1}$):