The correct answer is option 1, Mrs. Sarojini Naidu. She was the first woman to become a Governor of an Indian state. Sarojini Naidu was appointed as the Governor of Uttar Pradesh in 1947. She was a prominent political leader and also a renowned poet.

Option 2, Mrs. Sucheta Kriplani, was a notable freedom fighter and political activist, but she did not serve as a Governor.

Option 3, Mrs. Indira Gandhi, was the first and only female Prime Minister of India. She did not hold the position of Governor.

Option 4, Mrs. Vijaya Lakshmi Pandit, was the first woman to hold the position of President of the United Nations General Assembly. She also did not serve as a Governor.

Therefore, the correct answer is option 1, Mrs. Sarojini Naidu.