Option 1: Duarte Barbosa is not the correct answer. Duarte Barbosa was a Portuguese writer and explorer who traveled to India in the 16th century. However, he did return to Europe after his travels in India.

Option 2: Manucci is the correct answer. Niccolao Manucci, an Italian adventurer and memoirist, arrived in India in the late 17th century. He became a trusted physician to the Mughal emperor Aurangzeb and chose to settle in India permanently, serving in various roles in the Mughal court until his death. Manucci is known for his detailed accounts of life in India during that time.

Option 3: Jean-Baptiste Tavernier is not the correct answer. Tavernier, a French traveler and trader, made several voyages to India in the 17th century. While he spent a significant amount of time in India, he did return to Europe after his travels.

Option 4: Francois Bernier is not the correct answer. Bernier, a French physician and traveler, visited India in the 17th century and spent several years there. However, he eventually returned to Europe and continued his travels to other parts of the world.

In conclusion, the correct answer is option