What is the term used for the minimum kinetic energy required for the reactant molecules to undergo a chemical reaction?

What is the activation energy $(kJ \, mol^{-1})$ for a reaction if its rate constant doubles when the temperature is raised from $300 \, K$ to $400 \, K$ ? $(R = 8.314 \, J \, mol^{-1} \, K^{-1})$

The rate constants of a reaction at $500 \, K$ and $700 \, K$ are $0.02 \, s^{-1}$ and $0.07 \, s^{-1}$ respectively. Calculate the values of $E_{a}$ and $A$.

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 : $R = 2 \ cal \ K^{-1} \ mol^{-1}$)

Consider the following transformation involving first order elementary reactions in each step at constant temperature as shown below.
$A + B \underset{\text{Step } 3}{\overset{\text{Step } 1}{\rightleftharpoons}} C \xrightarrow{\text{Step } 2} P$
Some details of the above reaction are listed below.

Step	Rate constant $(s^{-1})$	Activation energy $(kJ \ mol^{-1})$
$1$	$k_1$	$300$
$2$	$k_2$	$200$
$3$	$k_3$	$Ea_3$

If the overall rate constant of the above transformation $(k)$ is given as $k = \frac{k_1 k_2}{k_3}$ and the overall activation energy $(E_a)$ is $400 \ kJ \ mol^{-1}$,then the value of $Ea_3$ is $\qquad$ $kJ \ mol^{-1}$ (nearest integer).

Which is a wrong statement?