What is the activation energy for a reaction if its rate doubles when the temperature is raised from $20 \,^{\circ}C$ to $35 \,^{\circ}C$ in $kJ \,mol^{-1}$? $(R = 8.314 \,J \,mol^{-1} \,K^{-1})$

The rate constant $(k)$ of a reaction is measured at different temperatures $(T),$ and the data are plotted in the given figure. The activation energy of the reaction in $kJ\, mol^{-1}$ is :
($R$ is gas constant)

Consider the following energy profile for the reaction $X + Y \rightarrow R + S$. Which of the following deductions about the reaction is not correct?

Who discovered collision theory? On which the collision theory is based?

In which of the following cases is the percentage increase in rate constant maximum?

$Case$	$E_a \ (kcal/mol)$	$Temp. \ Change \ (K)$
$I$	$40$	$200 - 210$
$II$	$80$	$200 - 210$
$III$	$40$	$300 - 310$
$IV$	$80$	$300 - 310$

For reaction $A \to B$,the rate constant $k_1 = A_1 e^{-E_{a_1} / (RT)}$ and for the reaction $X \to Y$ the rate constant $k_2 = A_2 e^{-E_{a_2} / (RT)}$. If $A_1 = 10^8$,$A_2 = 10^{10}$ and $E_{a_1} = 600 \ cal/mol$,$E_{a_2} = 1800 \ cal/mol$,then the temperature at which $k_1 = k_2$ is (Given : $R = 2 \ cal/K \cdot mol$)