Concept:
Indian philosophy has six orthodox schools known as Shad-Darshanas.
Each school is associated with a major sage or propounder.
Step 1: Match Nyaya.
Nyaya philosophy is associated with Gautama or Gotama.
So,
\[
A \rightarrow III
\]
Step 2: Match Samkhya.
Samkhya philosophy is associated with Kapila.
So,
\[
B \rightarrow I
\]
Step 3: Match Yoga.
Yoga philosophy is associated with Patanjali.
So,
\[
C \rightarrow IV
\]
Step 4: Match Purva Mimansa.
Purva Mimansa is associated with Jaimini.
So,
\[
D \rightarrow II
\]
Thus, the correct matching is:
\[
A-III,\ B-I,\ C-IV,\ D-II
\]
Hence:
\[
\boxed{\text{(B)}}
\]