For the following parallel chain reaction,what will be the value of the overall half-life of $A$ in minutes?
Given that $\frac{[B]_t}{[C]_t} = \frac{16}{9}$
$A \xrightarrow{k_1 = 2 \times 10^{-3} \ s^{-1}} 4B$
$A \xrightarrow{k_2} C$

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 .............

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?

Fill in the blanks:
$(1)$ If $t_{1/2} = \frac{0.693}{k}$,then the order of reaction is .......... .
$(2)$ For a zero order reaction,$t_{1/2}$ is proportional to .......... of the initial concentration.
$(3)$ In a first order reaction,the rate of reaction is proportional to the .......... exponent of the concentration of the reactant.

Under identical reaction conditions,the concentration of a substance is $1.386 \ mol \ m^{-3}$. It is halved in $40 \ s$ and $20 \ s$ by first-order and zero-order kinetics,respectively. The ratio of the rate constants for the first-order $(k_1)$ and zero-order $(k_0)$ reactions,$\left( \frac{k_1}{k_0} \right)$,is ............ $m^3 \ mol^{-1}$.

For a first order reaction,which of the following statements is correct?