To answer this question, we need to have knowledge about the historical events related to Goa and the Portuguese presence in India.
Option A) 17th - This option is incorrect because Portuguese merchants first landed in Goa before the 17th century.
Option B) 14th - This option is incorrect because Portuguese merchants did not land in Goa in the 14th century.
Option C) 15th - This option is correct. Portuguese merchants first landed in Goa in the 15th century. In 1498, the Portuguese explorer Vasco da Gama arrived in India and established a trade route, leading to the Portuguese colonization of Goa.
Option D) 16th - This option is incorrect because Portuguese merchants landed in Goa before the 16th century.
The correct answer is C) 15th. This option is correct because Portuguese merchants first landed in Goa in the 15th century, with Vasco da Gama's arrival in 1498.