The correct answer is: A. Gulbadan Begum.
Gulbadan Begum was the daughter of Babur, the founder of the Mughal Empire, and his wife Maham Begum. She was born in 1522 in Kabul, Afghanistan. Gulbadan Begum was a close companion of her father and accompanied him on many of his campaigns. She also wrote an autobiography, Humayun Nama, which is an important source of information about the early Mughal period.
Noorjahan Begum was the wife of Jahangir, the third Mughal emperor. She was a powerful and influential figure at the Mughal court. Noorjahan Begum was not known to have written any historical accounts.
Jahanara Begum was the daughter of Jahangir and Mumtaz Mahal. She was a poet and writer. Jahanara Begum is not known to have written any historical accounts.
Zebun-nissah Begum was the daughter of Shah Jahan, the fifth Mughal emperor. She was a poet and writer. Zebun-nissah Begum is not known to have written any historical accounts.
Gulbadan Begum was the only one of the four ladies who wrote an historical account during the Mughal period.