Step 1:
Šiksā deals with pronunciation and phonetics.
\[
A \rightarrow II
\]
Kalpa explains ritualistic procedures and karmakāņda.
\[
B \rightarrow I
\]
Step 2:
Vyākaraņa is called the mouth of the Vedas.
\[
C \rightarrow IV
\]
Step 3:
Nirukta explains derivation and etymology of words.
\[
D \rightarrow III
\]
Step 4:
Thus, the correct sequence is:
\[
A-II,\; B-I,\; C-IV,\; D-III
\]
Hence, the correct answer is:
\[
\boxed{\text{(3)}}
\]