The rate constant of a reaction is $0.69 \times 10^{-1} \ min^{-1}$ and the initial concentration is $0.2 \ mol \ L^{-1}.$ The half-life period is ........ $\sec$

If the half-life $(t_{1/2})$ of a reaction is $69.3 \ s$ and the rate constant $(k)$ is $10^{-2} \ s^{-1}$,then the order of the reaction is:

For a certain first order reaction,$32 \%$ of the reactant is left after $570 \ s$. The rate constant of this reaction is ........... $\times 10^{-3} \ s^{-1}$. (Round off to the Nearest Integer).
$[$Given: $\log_{10} 2 = 0.301, \ln 10 = 2.303]$

$A$ and $B$ decompose via first order kinetics with half-lives $54.0 \, min$ and $18.0 \, min$ respectively. Starting from an equimolar non-reactive mixture of $A$ and $B$,the time taken for the concentration of $A$ to become $16$ times that of $B$ is ...... $min.$ (Round off to the Nearest Integer).

The time required for a first-order reaction to be $90\%$ complete is approximately .........

In the following first order reactions $A$ $\xrightarrow{K_1} B$ $\xrightarrow{K_2} \text{Product}$,find the ratio $K_1/K_2$ if $90\%$ of $A$ has been reacted in time $t$ while $99\%$ of $B$ has been reacted in time $2t$.