When the temperature changes from $293 \ K$ to $313 \ K$,the rate of a certain reaction becomes four times. Find the activation energy of the reaction in $kJ \ mol^{-1}$. $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?

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?

Explain the collision theory of chemical reactions.

For a reaction,given below is the graph of $\ln k$ vs $\frac{1}{T}$. The activation energy for the reaction is equal to $...... \ cal \ mol^{-1}$. (Nearest integer). (Given : $R = 2 \ cal \ K^{-1} \ mol^{-1}$)

Assertion : According to transition state theory for the formation of an activated complex,one of the vibrational degrees of freedom is converted into a translational degree of freedom.
Reason : Energy of the activated complex is higher than the energy of reactant molecules.