The correct answer is: B) 18th-20th centuries.
The Asaf Jahi dynasty, also known as the Nizams, ruled Hyderabad State from 1724 to 1948. The dynasty was founded by Mir Qamar-ud-din Khan, who was appointed as the Nizam of Hyderabad by the Mughal emperor Muhammad Shah. The Nizams were a powerful and influential dynasty, and they played a major role in the history of India.
Option A is incorrect because the Asaf Jahi dynasty did not rule Hyderabad State in the 16th-18th centuries. The Qutb Shahi dynasty ruled Hyderabad State during this time period.
Option C is incorrect because the Asaf Jahi dynasty did not rule Hyderabad State in the 17th-19th centuries. The Nizams ruled Hyderabad State from 1724 to 1948.
Option D is incorrect because the Asaf Jahi dynasty did not rule Hyderabad State in the 19th-20th centuries. The Nizams ruled Hyderabad State from 1724 to 1948.