Match the rate expressions in List-$I$ for the decomposition of $X$ with the corresponding profiles provided in List-$II$. $X_s$ and $k$ are constants having appropriate units.

Half-lives of a first order and a zero order reaction are same. Then the ratio of the initial rates of first order reaction to that of the zero order reaction is

The reaction $A \xrightarrow{K} \text{Product}$ is zero order while the reaction $B \xrightarrow{K} \text{Product}$ is first order. For what initial concentration of $A$,the half-lives of the two reactions will be equal?

An example of an autocatalytic reaction is:

$t_{100\%}$ is the time required for the $100\%$ completion of the reaction, while $t_{1/2}$ is the time required for $50\%$ of the reaction to be completed. Which of the following options correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first-order reactions, respectively?

Given below are two statements: $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$ and $1 \text{ cal} = 4.2 \text{ J}$.
Statement $I$: When $E_a = 12.6 \text{ kcal/mol}$, the room temperature rate constant is doubled by a $10 \text{ }^\circ\text{C}$ increase in temperature ($298 \text{ K}$ to $308 \text{ K}$).
Statement $II$: For a first-order reaction $A \to B$, the graph of half-life $(t_{1/2})$ versus initial concentration $[A]_o$ is a straight line passing through the origin.
In the light of the above statements, choose the correct answer from the options given below: