Step 1: Recall the concept of electron affinity.
The process
\[
X(g)+e^-\rightarrow X^-(g)
\]
is generally exothermic for non-metals because energy is released when an electron is added.
Step 2: Identify the exceptional case.
Noble gases have completely filled electronic configurations.
Adding an electron to xenon requires energy, so the process is endothermic.
Hence,
\[
\mathrm{Xe(g)+e^-\rightarrow Xe^-(g)}
\]
is an endothermic process.
Step 3: Write the answer.
Hence,
\[
\boxed{\mathrm{Xe(g)+e^-\rightarrow Xe^-(g)}}.
\]
Thus,
\[
\boxed{(A)}
\]
is the correct answer.