The rate of a first order reaction doubles when the temperature changes from $300 \ K$ to $310 \ K$. The activation energy of the reaction (in $kJ \ mol^{-1}$) is
$R=8.3 \ J \ K^{-1} \ mol^{-1}, \log 2=0.3$ (in $.33$)

When the temperature changes from $20\,^oC$ to $50\,^oC$,the rate of reaction becomes three times. The activation energy $(E_a)$ for the reaction is $.... \, kJ \, mol^{-1}$ $(R = 8.314 \, J \, K^{-1} \, mol^{-1})$.

At temperature $T \ K$,the rate constant of a reaction is $1/10$th of the rate constant at temperature $2T \ K$. What will be the activation energy of this reaction (in $RT$)?

Activation energy is defined as:

All energetically effective collisions do not result in a chemical change. Explain with the help of an example.

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?