For a first order reaction,the slope of the graph of $\log_{10}[A]_t$ versus time is equal to:

For a first order reaction,the half-life period is $5 \ min$. What time will it take for $99.9 \%$ completion of the reaction (in $min$)?

$A$ flask is filled with equal moles of $A$ and $B$. The half-lives of $A$ and $B$ are $100 \, s$ and $50 \, s$ respectively and are independent of the initial concentration. The time required for the concentration of $A$ to be four times that of $B$ is $.... \, s.$
(Given : $\ln 2 = 0.693$ )

Two first order reactions have half-lives in the ratio $3 : 2$. Calculate the ratio of time intervals $t_1 : t_2$ if $t_1$ is the time period for $25\%$ completion of the first reaction and $t_2$ for $75\%$ completion of the second reaction. (in $: 1$)

What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is $10 \ minute$?

For a first-order reaction,if $75\%$ of the reaction is completed in $15 \ min$,then the time required for $90\%$ completion of the reaction will be ........... $min$.