If the decomposition reaction $A_{(g)} \longrightarrow B_{(g)}$ follows first-order kinetics,then the graph of the rate of formation of $B$,denoted by $R$,against time $t$ will be:

Which of the following graphs represent a first order reaction ($a =$ initial concentration of reactant,$x =$ concentration of reactant consumed,$t =$ time)?

The ratio of $t_{0.75}$ and $t_{0.5}$ for a first-order reaction is:

Time required for completion of $99.9 \%$ of a First order reaction is . . . . . . times of half life $(t_{1/2})$ of the reaction.

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

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 .... .