$A$ first-order reaction takes $30$ minutes for $75\%$ decomposition. Calculate its rate constant. (in $\text{ min}^{-1}$)

The units of rate constant for a first-order reaction are:

Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

Thermal decomposition of $HCOOH$ is a first order reaction and the rate constant at $T(K)$ is $4.606 \times 10^{-3} \ s^{-1}$. The time required to decompose $90 \%$ of initial quantity of $HCOOH$ at $T(K)$ in seconds is

$A$ first order reaction is half completed in $45 \, \text{minutes}$. How long does it need for $99.9 \%$ of the reaction to be completed? (in $hr$)

The initial rate for a first order reaction is $0.6932 \times 10^{-2} \ mol \ L^{-1} \ min^{-1}$ and the initial concentration of the reactant is $0.1 \ M$. Then $t_{1/2}$ is equal to ...... $min$.