The correct answer is: a) Shaivite temples.
The Sethupathis of Ramanathapuram were a Hindu dynasty that ruled the Ramanathapuram region of Tamil Nadu from the 13th to the 18th centuries. They were patrons of Shaivite temples, and many of the temples in the region were built or renovated by them. The most famous of these temples is the Ramanathaswamy Temple, which is one of the most important pilgrimage sites in Hinduism.
The Sethupathis were also patrons of art and literature. They commissioned many works of art, including sculptures, paintings, and murals. They also patronized Tamil literature, and many of the most famous Tamil poets of the period were patronized by the Sethupathis.
The Sethupathis were a powerful and influential dynasty, and their patronage of Shaivite temples and art and literature had a lasting impact on the region.
Option b) is incorrect because the Sethupathis were Hindu, not Jain.
Option c) is incorrect because the Sethupathis were not patrons of Mughal architecture.
Option d) is incorrect because the Sethupathis were not patrons of European-style palaces.