Concept:
Indian philosophical schools explain causation in different ways.
The relation between cause and effect is a major topic in Indian metaphysics.
Step 1: Match Jainism.
Jainism is associated with Sadasatkaryavada.
It holds a complex view in which an effect may be understood through both being and non-being in different respects.
So:
\[
A \rightarrow III
\]
Step 2: Match Nyaya-Vaisheshika.
Nyaya-Vaisheshika accepts eternal atoms as material causes.
So, it is connected with:
\[
\text{Nitya paramanu karanavada}
\]
Thus:
\[
B \rightarrow I
\]
Step 3: Match Ramanuja.
Ramanuja's Vishishtadvaita accepts Brahman as the real cause of the world.
The world is a real transformation of Brahman.
So:
\[
C \rightarrow IV
\]
Step 4: Match Shankara.
Shankara's Advaita Vedanta explains the world as apparent manifestation.
This is known as:
\[
\text{Brahma Vivartavada}
\]
So:
\[
D \rightarrow II
\]
Step 5: Final matching.
The correct matching is:
\[
A-III,\ B-I,\ C-IV,\ D-II
\]
Hence:
\[
\boxed{\text{(A)}}
\]