Step 1: Understanding the Vedanta schools and their proponents.
- Dvaita (dualism) was propounded by Madhva, so (a) matches with (iii).
- Śuddhādvaita (pure non-dualism) was taught by Rāmānuja, so (b) matches with (ii).
- Advaita (non-dualism) was propounded by Śankara, so (c) matches with (i).
- Viśiṣṭādvaita (qualified non-dualism) was taught by Nimbārka, so (d) matches with (iv).
Step 2: Analyzing the options.
- (A) (a) and (iii): Correct, as Dvaita is associated with Madhva.
- (B) (d) and (ii): Correct, as Viśiṣṭādvaita is associated with Rāmānuja.
- (C) (b) and (i): Incorrect, as Śuddhādvaita is associated with Rāmānuja, not Śankara.
- (D) (c) and (iv): Incorrect, as Advaita is associated with Śankara, not Nimbārka.
Step 3: Conclusion.
The correct answers are (A) and (B), which correctly match the Vedanta schools with their proponents.