Option-1: Aditya-I was the first ruler of the Chola dynasty, but there is no evidence to suggest that he conquered Ceylon.

Option-2: Rajaraja-I is the correct answer. He is known for his conquest of Ceylon in the 10th century. His successful invasion of Ceylon resulted in the establishment of Chola control over the island.

Option-3: Rajendra was the son of Rajaraja-I and continued his father`s conquests, including the invasion of Ceylon. However, Rajaraja-I was the one who conquered Ceylon first.

Option-4: Vijayalaya was the founder of the Chola dynasty, but there is no historical evidence to suggest that he conquered Ceylon.

Therefore, the correct answer is option-2, Rajaraja-I.