Hyderabad State became part of independent India in 1948 through:

Negotiated settlement
Military operation (Operation Polo)
Popular referendum
Act of the British Parliament

The correct answer is: B) Military operation (Operation Polo)

Hyderabad State was a princely state in India that existed from 1724 to 1948. It was ruled by the Nizams, who were Muslim. After the independence of India in 1947, the Nizam wanted to remain independent. However, the Indian government wanted Hyderabad to join India. This led to a conflict between the two sides.

In September 1948, the Indian government launched a military operation called Operation Polo to annex Hyderabad. The Nizam surrendered on September 17, 1948, and Hyderabad became part of India.

Option A: Negotiated settlement is not the correct answer because the Nizam did not want to negotiate with the Indian government. He wanted to remain independent.

Option C: Popular referendum is not the correct answer because there was no popular referendum held on whether Hyderabad should join India or remain independent.

Option D: Act of the British Parliament is not the correct answer because the British Parliament did not pass any act that made Hyderabad part of India.