The Qutb Shahi dynasty, known for its patronage of arts and culture, ruled over:

Golconda Sultanate
Bidar Sultanate
Ahmadnagar Sultanate
Berar Sultanate

The correct answer is: A) Golconda Sultanate.

The Qutb Shahi dynasty was a Muslim dynasty that ruled the Golconda Sultanate in the Deccan region of India from 1518 to 1687. The dynasty was founded by Quli Qutb Shah, a Turk who had served as a general in the Bahmani Sultanate. Quli Qutb Shah declared himself independent in 1518 and established his capital at Golconda.

The Qutb Shahi dynasty was known for its patronage of arts and culture. The Qutb Shahi rulers built many beautiful palaces, mosques, and tombs. They also supported the arts of painting, music, and literature.

The Qutb Shahi dynasty came to an end in 1687 when the Mughal emperor Aurangzeb conquered Golconda.

The other options are incorrect because they refer to different sultanates. The Bidar Sultanate was a Muslim sultanate that ruled in the Deccan region of India from 1489 to 1527. The Ahmadnagar Sultanate was a Muslim sultanate that ruled in the Deccan region of India from 1490 to 1636. The Berar Sultanate was a Muslim sultanate that ruled in the Deccan region of India from 1572 to 1616.