The correct answer is A. The Gol Gumbaz in Vijayapura (Bijapur) was built during the rule of the Adil Shahi dynasty.
The Adil Shahi dynasty was a Muslim dynasty that ruled the Deccan region of India from the 15th to the 17th centuries. The dynasty was founded by Yusuf Adil Shah, a Turk who came to India as a mercenary in the service of the Bahmani Sultanate. Yusuf Adil Shah declared himself independent in 1489 and established his capital at Bijapur.
The Adil Shahi dynasty was known for its patronage of art and architecture. The Gol Gumbaz is one of the most famous monuments of the Adil Shahi period. It is a mausoleum that was built by Muhammad Adil Shah II in the 17th century. The Gol Gumbaz is the largest dome in India and the second largest dome in the world. It is also one of the most acoustically perfect buildings in the world.
The other options are incorrect. The Bahamani Sultanate was a Muslim sultanate that ruled the Deccan region of India from the 14th to the 16th centuries. The Wodeyars of Mysore were a Hindu dynasty that ruled the Mysore region of India from the 14th to the 19th centuries. The Chalukyas of Badami were a Hindu dynasty that ruled the Deccan region of India from the 6th to the 8th centuries.