Concept:
India hosts several renowned dance festivals associated with particular states and historical cultural centers. These festivals promote Indian classical dance traditions and attract artists from across the country.
Step 1: Match Khajuraho Dance Festival.
\[
\text{Khajuraho Dance Festival}
\]
is held in:
\[
\text{Madhya Pradesh}
\]
Thus:
\[
A \rightarrow III
\]
Step 2: Match Modhera Dance Festival.
\[
\text{Modhera Dance Festival}
\]
is celebrated in:
\[
\text{Gujarat}
\]
Thus:
\[
B \rightarrow I
\]
Step 3: Match Neeshagandhi Dance Festival.
\[
\text{Neeshagandhi Dance Festival}
\]
is associated with:
\[
\text{Kerala}
\]
Thus:
\[
C \rightarrow IV
\]
Step 4: Match Konark Dance Festival.
\[
\text{Konark Dance Festival}
\]
is held in:
\[
\text{Orissa (Odisha)}
\]
Thus:
\[
D \rightarrow II
\]
Step 5: Write the final matching sequence.
The correct matching is:
\[
A\text{-}III,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}II
\]
Step 6: Compare with the given options.
Among the given choices:
\[
(A)\ A\text{-}I,\ B\text{-}II,\ C\text{-}III,\ D\text{-}IV
\]
\[
(B)\ A\text{-}II,\ B\text{-}III,\ C\text{-}I,\ D\text{-}IV
\]
\[
(C)\ A\text{-}III,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}II
\]
\[
(D)\ A\text{-}IV,\ B\text{-}III,\ C\text{-}I,\ D\text{-}II
\]
the correct answer is:
\[
\boxed{A\text{-}III,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}II}
\]
Hence:
\[
\boxed{\mathrm{(C)}}
\]