The correct answer is: A) Mughal Empire.
The Nizams of Hyderabad were initially vassals of the Mughal Empire. The Mughal Empire was a Muslim empire that ruled over much of the Indian subcontinent from the 16th to the 18th centuries. The Nizams of Hyderabad were a Muslim dynasty that ruled over the Hyderabad State in southern India from the 18th to the 20th centuries. The Nizams were initially vassals of the Mughal Empire, but they became independent in the 18th century. The Nizams of Hyderabad were a powerful and wealthy dynasty, and they played an important role in the history of India.
The other options are incorrect. The Maratha Empire was a Hindu empire that ruled over much of the Indian subcontinent in the 18th and 19th centuries. The British Empire was a European empire that ruled over much of the world in the 19th and 20th centuries. The Bahmani Sultanate was a Muslim sultanate that ruled over much of the Deccan Plateau in southern India from the 14th to the 16th centuries.