Explanation:

- Lakshmi Kant Jha: He served as the Governor of Jammu & Kashmir from 1973 to 1981. His term lasted around 8 years, making him one of the longer-serving governors in an Indian state.

- Padmaja Naidu: She served as the Governor of West Bengal from 1956 to 1967. Her term lasted for about 11 years.

- N D Tiwari: Known for his political services but was not the longest-serving governor in any state. He served as the Governor of Andhra Pradesh and Uttarakhand for shorter durations.

- Sarojini Naidu: She was the first woman to become a governor in India, serving in Uttar Pradesh from 1947 to 1949.

- The correct answer is option 2, Padmaja Naidu, as she served for about 11 years.