The correct reaction profile diagram for a positive catalyst reaction.

For an exothermic reaction,the following two steps are involved:
Step $1$: $A + B \to I$ $(slow)$
Step $2$: $I \to AB$ $(fast)$
Which of the following graphs correctly represents this reaction?

If the definition of the temperature coefficient of the reaction holds good for a reaction between $27^{\circ} C$ and $37^{\circ} C$,the activation energy for the reaction in $kJ \cdot mol^{-1}$ is

For a reaction,the graph of $\ln k$ (on y-axis) and $1 / T$ (on x-axis) is a straight line with a slope $-2 \times 10^4 \ K$. The activation energy of the reaction (in $kJ \ mol^{-1}$) is $(R = 8.3 \ J \ K^{-1} \ mol^{-1})$

Consider a complex reaction taking place in three steps with rate constants $k_1$,$k_2$,and $k_3$ respectively. The overall rate constant $k$ is given by the expression $k = \sqrt{\frac{k_1 k_3}{k_2}}$. If the activation energies of the three steps are $60$,$30$,and $10 \ kJ \ mol^{-1}$ respectively,then the overall energy of activation in $kJ \ mol^{-1}$ is $..........$ $(Nearest \ integer)$

$A \rightarrow B$ (first reaction)
$C \rightarrow D$ (second reaction)
Consider the above two first-order reactions. The rate constant for the first reaction at $500 \ K$ is double of the same at $300 \ K$. At $500 \ K, 50 \%$ of the reaction becomes complete in $2 \ hours$. The activation energy of the second reaction is half of that of the first reaction. If the rate constant at $500 \ K$ of the second reaction is double the rate constant of the first reaction at the same temperature, then the rate constant for the second reaction at $300 \ K$ is . . . . . . $\times 10^{-1} \ hour^{-1}$ (nearest integer).