The Qutb Shahi Dynasty ruled over the Golconda Sultanate, with their capital at:

The correct answer is: a) Hyderabad.

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, who was a Turk from Central Asia. The Qutb Shahis were a powerful and influential dynasty, and they built many beautiful monuments and buildings in Hyderabad, their capital city. The Qutb Shahi dynasty came to an end in 1687, when the Mughal emperor Aurangzeb conquered the Golconda Sultanate.

The other options are incorrect because they were not the capital of the Golconda Sultanate. Warangal was the capital of the Kakatiya dynasty, Bidar was the capital of the Bahmani Sultanate, and Bijapur was the capital of the Adilshahi dynasty.