Concept:
Different Indian classical dance forms have distinct repertoire items and performance components. These items are characteristic features of their respective dance traditions.
Step 1: Match Allaripu.
\[
\text{Allaripu}
\]
is the opening invocatory item of:
\[
\text{Bharata Natyam}
\]
Thus:
\[
A \rightarrow III
\]
Step 2: Match Chollakettu.
\[
\text{Chollakettu}
\]
is the opening item in:
\[
\text{Mohini Attam}
\]
Thus:
\[
B \rightarrow IV
\]
Step 3: Match Gathbhav.
\[
\text{Gathbhav}
\]
is an expressive storytelling component associated with:
\[
\text{Kathak}
\]
Thus:
\[
C \rightarrow I
\]
Step 4: Match Moksha.
\[
\text{Moksha}
\]
is the concluding item of:
\[
\text{Odissi}
\]
Thus:
\[
D \rightarrow II
\]
Step 5: Write the final matching sequence.
The correct matching is:
\[
A\text{-}III,\ B\text{-}IV,\ C\text{-}I,\ D\text{-}II
\]
Step 6: Compare with the given options.
Among the given choices:
\[
(A)\ A\text{-}I,\ B\text{-}IV,\ C\text{-}II,\ D\text{-}III
\]
\[
(B)\ A\text{-}II,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}III
\]
\[
(C)\ A\text{-}IV,\ B\text{-}III,\ C\text{-}II,\ D\text{-}I
\]
\[
(D)\ A\text{-}III,\ B\text{-}IV,\ C\text{-}I,\ D\text{-}II
\]
the correct answer is:
\[
\boxed{A\text{-}III,\ B\text{-}IV,\ C\text{-}I,\ D\text{-}II}
\]
Hence:
\[
\boxed{\mathrm{(D)}}
\]