The slope of the graph between rate ($Y$-axis) and $[A]$ ($X$-axis) for a first-order reaction is equal to:

The rate for a first order reaction is $0.6932 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$ and the initial concentration of the reactants is $1 \, M$. The half-life $T_{1/2}$ is equal to ........ $min$.

In a first order reaction,the concentration of the reactant decreases from $20 \ mmol \ dm^{-3}$ to $8 \ mmol \ dm^{-3}$ in $40 \ minute$. Find the rate constant of the reaction.

What is the numerical value of the rate constant of a first-order reaction that is $20 \%$ completed in $10 \ min$ (in $min^{-1}$)?

$A$ 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 : $\ln 2 = 0.693$ )

Time required to decompose $SO_2Cl_2$ to half of its initial amount is $60 \ min$. If the decomposition is a first order reaction,calculate the rate constant of the reaction. (in $min^{-1}$)