Under the same reaction conditions, initial concentration of $1.386 \ mol \ dm^{-3}$ of a substance becomes half in $40 \ s$ and $20 \ s$ through first-order and zero-order kinetics respectively. Ratio $\left(\frac{k_{1}}{k_{0}}\right)$ of the rate constants for first-order $\left(k_{1}\right)$ and zero-order $\left(k_{0}\right)$ of the reactions is

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:

Which of the following statements is correct?

The rate constant for the first order decomposition of $H_{2}O_{2}$ is given by the following equation:
$\log k = 14.34 - 1.25 \times 10^{4} \, K / T$
Calculate $E_{a}$ for this reaction and at what temperature will its half-period be $256 \, min$?

An example of an autocatalytic reaction is:

Which of the following graphs is incorrect for a first-order reaction? $A \rightarrow B$