The correct answer is option 3: Sucheta Kripalani. Sucheta Kripalani was the first woman to become a Chief Minister of any state in India. She served as the Chief Minister of Uttar Pradesh from 1963 to 1967. It is important to note that she is also the first woman in India to hold the position of a Chief Minister.

Option 1: Nandini Satpathy was a prominent Indian politician and writer, but she was not the first woman to become a Chief Minister of any state in India.

Option 2: Dr. J. Jayalalitha was a renowned politician and the Chief Minister of Tamil Nadu. While she was a significant figure in Indian politics, she was not the first woman to hold the position of Chief Minister.

Option 4: Ms. Mayawati, also known as Kumari Mayawati, is a well-known Indian politician. However, she was not the first woman to become a Chief Minister in India.

Therefore, the correct answer is option 3: Sucheta Kripalani.