Option 1: Mrs. Sarojini Naidu

Mrs. Sarojini Naidu was indeed the first woman Governor of a state in free India. She was appointed as the Governor of the United Provinces (now Uttar Pradesh) in 1947. She was not only a politician but also a poet and played a significant role in the Indian independence movement.

Option 2: Mrs. Sucheta Kriplani

Mrs. Sucheta Kriplani was a prominent freedom fighter and politician, but she did not serve as a Governor of a state. She was the first woman Chief Minister of a state, serving as the Chief Minister of Uttar Pradesh from 1963 to 1967.

Option 3: Mrs. Indira Gandhi

Mrs. Indira Gandhi, the daughter of Jawaharlal Nehru, was the first and only woman Prime Minister of India. She did not hold the position of a Governor.

Option 4: Mrs. Vijay Laxmi Pandit

Mrs. Vijay Laxmi Pandit, sister of Jawaharlal Nehru, was a diplomat and politician. She served as the Ambassador of India to the United States and United Kingdom. However, she did not serve as a Governor.

Therefore