The correct answer is (B) Rashsundari Devi.
In East Bengal, in the early nineteenth century, Rashsundari Devi, a young married girl in a very orthodox household, learnt to read secretly and wrote her autobiography Amar Jiban, published in 1876.
Source: Chapter 5, Section 8.1 – Women and Print
The passage clearly states it was Rashsundari Devi (also spelled Rashsundari Debi in the source), not Pandita Ramabai or Tarabai Shinde (who wrote about widows in Maharashtra in the 1880s), nor Kailashbashini Debi (who wrote from the 1860s about women's imprisonment at home). The key identifiers in the question — "beginning of 19th century," "orthodox household," "Amar Jiban" — all point directly to Rashsundari Devi.