After Independence, the Indian Government took over Hyderabad, the State of Nizam, through military action. This means that the Indian armed forces were used to forcibly compel the Nizam and his administration to surrender their control and submit to the authority of the Indian government. Police action refers to the use of police forces to maintain law and order, but in this case, it was the military that was involved. Persuasion and negotiations involve peaceful means of reaching an agreement, which did not happen in this situation. Therefore, option 2, military action, is the correct answer. It is important to note that forceful takeover of states was rare, with most princely states willingly acceding to the Indian Union.