$A$ first order reaction is $25 \%$ completed in $40 \ min$. What is the rate constant $k$ for the reaction?

Azo isopropane decomposes according to the equation:
$((CH_3)_2CHN)_2N_{2(g)} \xrightarrow{250 - 290 \ ^oC} N_{2(g)} + C_6H_{14(g)}$
It is found to be a first order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,then the rate constant $K$ is given by:

What is the rate constant of a first-order reaction if $0.08 \ mol$ of reactant reduces to $0.02 \ mol$ in $23.03 \ min$ (in $min^{-1}$)?

Consider the first order reaction $R \to P$. The fraction of molecules decomposed in the given first order reaction can be expressed as:

For a first-order reaction,the rate constant is $60 \ s^{-1}$. How much time will it take for the initial concentration of the reactant to be reduced to $1/10$th of its initial value?

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 $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$