The correct answer is (a) Kulottunga I.
Kulottunga I was the Chola emperor who ruled from 1070 to 1118 CE. He was a powerful and successful ruler who expanded the Chola empire to its greatest extent. He also made significant contributions to the arts and literature.
In 1077 CE, Kulottunga I invaded Sri Lanka and defeated the Sinhalese king Vijayabahu I. He then married his daughter to the Sinhalese prince Virabahu I, thus establishing a peaceful relationship between the two kingdoms.
Kulottunga I was a wise and just ruler who was loved by his subjects. He is considered to be one of the greatest Chola emperors.
The other options are incorrect for the following reasons:
(b) Rajendra I was the Chola emperor who ruled from 1014 to 1044 CE. He was the son of Rajaraja I and the father of Kulottunga I. He was a powerful and successful ruler who expanded the Chola empire to its greatest extent. However, he did not invade Sri Lanka or marry his daughter to a Sinhalese prince.
(c) Adhirajendra was the Chola emperor who ruled from 1044 to 1052 CE. He was the son of Rajendra I and the brother of Kulottunga I. He was a powerful and successful ruler who expanded the Chola empire to its greatest extent. However, he did not invade Sri Lanka or marry his daughter to a Sinhalese prince.
(d) Rajadhiraja was the Chola emperor who ruled from 1052 to 1064 CE. He was the son of Adhirajendra and the nephew of Kulottunga I. He was a powerful and successful ruler who expanded the Chola empire to its greatest extent. However, he did not invade Sri Lanka or marry his daughter to a Sinhalese prince.