Which of the following graphs between the rate constant $(k)$ and temperature $(T)$ represents the Arrhenius equation?

Collision theory is used to explain how chemical species undergo a reaction. Using this theory and the kinetic molecular model,which of the following does $NOT$ influence the rate of a chemical reaction?

The half-life periods of a first order reaction at $300 \ K$ and $400 \ K$ are $50 \ s$ and $10 \ s$ respectively. The activation energy of the reaction in $kJ \ mol^{-1}$ is $(\log 5 = 0.70)$

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.

For a first-order reaction $A \to P$,the rate constant equation is given by $\log K = -2000 \, (1/T) + 6.0$. The pre-exponential factor $A$ and the activation energy $E_a$ are,respectively:

According to the Arrhenius equation,which of the following statements are correct?
$(A)$ $A$ high activation energy usually implies a fast reaction.
$(B)$ Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
$(C)$ Higher the magnitude of activation energy,stronger is the temperature dependence of the rate constant.
$(D)$ The pre-exponential factor is a measure of the rate at which collisions occur,irrespective of their energy.