Explanation:

- Option 1: Banabhatta

- Correct Answer. Banabhatta was a 7th-century Sanskrit scholar and poet in the court of Emperor Harsha. He authored 'Harshacharita', a biography of Harsha.

- Option 2: Swami Sivananda

- Swami Sivananda was a spiritual teacher and a proponent of yoga and Vedanta in the 20th century. He did not write 'Harshacharita'.

- Option 3: Valmiki

- Valmiki is revered as the author of the ancient Indian epic, the Ramayana. He lived long before Harsha's time.

- Option 4: Rabindranath Tagore

- Tagore was a Bengali polymath who reshaped Indian literature and music in the late 19th and early 20th centuries. He did not write 'Harshacharita'.