The half-life period of a first-order reaction is $138.6 \ min$. The rate constant of the reaction is: (in $min^{-1}$)

For the reaction $2A + B \to \text{Product}$,the rate law is given as $\frac{-d[A]}{dt} = K[A]$. At a time when $t = \frac{1}{K}$,the concentration of the reactant $A$ is ($Co =$ initial concentration).

For a first order reaction $A \rightarrow \text{Products}$,initial concentration of $A$ is $0.1 \, M$,which becomes $0.001 \, M$ after $5 \, \min$. Rate constant for the reaction in $\min^{-1}$ is .... .

The value of the velocity constant for a first-order reaction is $3.46 \times 10^{-3} \ min^{-1}$. The time for half-change is ........ $min$.

For a first order reaction,the ratio of the time for $75 \% $ completion of a reaction to the time for $50 \% $ completion is $....$ . (Integer answer)

$A$ first-order reaction starts with a decimolar solution of the reactant. After $8$ minutes,its concentration becomes $M/100$. Calculate the rate constant of the reaction.