Which among the following equations represents the Arrhenius equation?

The equilibrium constant at $27\,^{\circ}C$ and $127\,^{\circ}C$ is $30$ and $40$ respectively. What will be the ratio of activation energy $(E_{a})_{f} / (E_{a})_{b}$?

$A$ reaction takes place in three steps with individual rate constant and activation energy as follows:

$Step$	$Rate \ constant$	$Activation \ energy$
$Step-1$	$k_1$	$E_{a1} = 180 \ kJ/mol$
$Step-2$	$k_2$	$E_{a2} = 80 \ kJ/mol$
$Step-3$	$k_3$	$E_{a3} = 50 \ kJ/mol$

If overall rate constant,$k = (\frac{k_1 k_2}{k_3})^{2/3}$,then overall activation energy of the reaction will be .......... $kJ/mol$.

$A$ mixture of $H_2$ and $O_2$ is very stable at room temperature. However,it explodes immediately upon sparking. This is because .........

Which equation is true to calculate the energy of activation,if the rate of reaction is doubled by increasing temperature from $T_1 \ K$ to $T_2 \ K$?

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 $(\log 5 = 0.70)$