Which of the following reaction mechanisms will have a fractional order with respect to $A_2$ or $B_2$?

If the half-life periods of a first-order reaction and a zero-order reaction are equal,then the ratio of the initial rates of the reactions will be .............

For any chemical reaction,what factors do chemists aim to determine?

Given below are two statements:
Statement $I$: The rate law for the reaction $A + B \rightarrow C$ is rate $(r) = k[A]^2[B]$. When the concentration of both $A$ and $B$ is doubled,the reaction rate is increased "$x$" times.
Statement $II$: The figure shows the variation in concentration against time plot for a "$y$" order reaction.
Concentration of $R$ vs Time plot: $A$ straight line with a negative slope equal to $-K$.
The value of $x + y$ is . . . . . .

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. The 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: