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 time taken for $10 \%$ completion of a first order reaction is $20$ minutes. The time required for the completion of $19 \%$ of the same reaction in minutes is

The half-life for radioactive decay of $^{14}C$ is $5730$ years. An archaeological artifact containing wood had only $80 \%$ of the $^{14}C$ found in a living tree. Estimate the age of the sample.

The reaction $A + B \xrightarrow{k}$ product is first order with respect to $A$ and zero order with respect to $B$. If $a_0$ and $a_t$ are the concentrations of $A$ at $t = 0$ and after time $t \, sec$ respectively,then select the correct relationship -

If the half-life of a first-order reaction is $4 \ min$,then after how many minutes will the reaction be $99.9 \%$ complete?