$A$ first order reaction is $60 \%$ complete in $20 \ min$. How long will the reaction take to be $84 \%$ complete (in $min$)?

$99 \%$ of a first order reaction was completed in $64 \text{ min}$. In how many minutes will $99.9 \%$ of the reaction be complete?

What is the slope of the graph plotted between half-life $(t_{1/2})$ and initial concentration $(a)$ for a $1^{st}$ order reaction?

An organic compound undergoes first order decomposition. The time taken for its decomposition to $\frac{1}{8}$ and $\frac{1}{10}$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}}$? $[\log 2 = 0.30]$

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 rate constant for a first order reaction is $20 \, min^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is $........ \times 10^{-2} \, min$. (Nearest integer) (Given: $\ln 10 = 2.303, \log 2 = 0.3010$)