Half-life of a first order reaction is $20 \ s$ and initial concentration of reactant is $0.2 \ M$. The concentration of reactant left after $80 \ s$ is (in $M$)

Calculate the rate constant of a first-order reaction if the concentration of the reactant decreases by $90 \%$ in $30 \ minutes$.

$A$ flask contains a mixture of compounds $AB$ and $XY$. Both decompose by first-order kinetics upon heating. If the half-life periods of $AB$ and $XY$ are $30 \ min$ and $10 \ min$ respectively,how many minutes will it take for the concentration of $AB$ to be four times the concentration of $XY$? (Assume initial concentrations of $AB$ and $XY$ are equal.)

The units of rate constant for a first-order reaction are:

$A$ 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.

Which is the correct relation between rate constant and half-life of a first-order reaction?