For a first-order reaction, $20 \text{ mmol}$ of reactant is reduced to $10 \text{ mmol}$ in $1.151 \text{ min}$. Find the rate constant $k$. (in $\text{ min}^{-1}$)

Assertion : For a first order reaction,$t_{1/2}$ is independent of initial concentration.
Reason : For a first order reaction,rate constant $k \propto [R]$.

Calculate the rate constant of the first order reaction if $80 \%$ of the reactant decomposes in $60 \ minutes$.

$A$ first-order reaction takes $16 \text{ minutes}$ for its $50\%$ completion. What fraction of the reactant would react in $32 \text{ minutes}$ from the beginning?

The rate constant for the oxidation of hydrogen peroxide by $KMnO_4$ is $6.93 \times 10^{-5} \ s^{-1}$. How much time will it take for the volume of a standard $KMnO_4$ solution to decrease from $20 \ mL$ to $8 \ mL$?

Identify True $(T)$ and False $(F)$ statements for the following expressions regarding a first-order reaction $R \rightarrow P$:
Statement $I$: $\text{Rate} = -\frac{d[R]}{dt} = k[R]$
Statement $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$