Step 1:
Brahmasutra was composed by Badarayana, while Mimamsasutra was written by Jaimini.
Step 2:
Nyayasutra is associated with:
\[
\boxed{\text{Gautama}}
\]
Step 3:
Vaisheshikasutra was authored by:
\[
\boxed{\text{Kanada}}
\]
Step 4:
Hence, the correct sequence is:
\[
A-III,\; B-IV,\; C-I,\; D-II
\]
Therefore, the correct answer is:
\[
\boxed{\text{(2)}}
\]