$A$ reaction has a half-life of $1 \, \text{min}$. The time required for $99.9 \, \%$ completion of the reaction is ......... $\text{min}$. (Round off to the nearest integer)
[Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

If the half-life $(t_{1/2})$ of a first-order reaction is $20 \ minutes$,what fraction of the reactant remains after $40 \ minutes$?

Dissociation of $N_2O_5$ dissolved in $CCl_4$ at constant temperature: $N_2O_{5(soln)} \to 2NO_{2(soln)} + \frac{1}{2}O_{2(g)}$. This is a first order reaction. The velocity constant is $5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$. How much time is required to produce $0.20 \ mol \ L^{-1}$ concentration of $NO_2$ (in $s$)?

Which of the following plots is(are) correct for the given reaction? $( [P]_0$ is the initial concentration of $P$ $)$

$A$ 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.)

In the reaction $2N_2O_5 \to 4NO_2 + O_2$,the initial pressure is $500 \ atm$ and the rate constant $K$ is $3.38 \times 10^{-5} \ s^{-1}$. After $10 \ minutes$,the final pressure of $N_2O_5$ is ........ $atm$.