Step 1: Recall the characteristics of each fermentation process.
\[
\boxed{
\begin{aligned}
\text{Batch} &\rightarrow \text{No input or output during operation}
\text{Fed-batch} &\rightarrow \text{Substrate added without product outflow}
\text{Continuous} &\rightarrow \text{Steady-state operation}
\text{Chemostat} &\rightarrow \text{Constant dilution rate}
\end{aligned}
}
\]
Step 2: Match List-I with List-II.
Thus,
\[
\boxed{
A-\mathrm{III},\;
B-\mathrm{II},\;
C-\mathrm{I},\;
D-\mathrm{IV}
}
\]
Therefore,
\[
\boxed{(A)}
\]
is the correct answer.