The correct options are
A Vijayalaya conquered Thanjavur and established it as the capital of the Medieval Chola Empire when the Pallava dynasty weakened.
B Aditya I established the Cholas as the main power in the Tamil Nadu region by decisively defeating the Pallavas.
C Both Rajaraja Chola I and Rajendra Chola I achieved multiple naval conquests and Rajendra Chola I extended the borders of the kingdom northwards.
The Cholas were feudal lords under the Pallavas. The Cholas, under Vijayalaya, rose to power when the Pallavas weakened. He conquered Thanjavur and established it as the capital of the Medieval Chola or Imperial Chola Empire. The second Chola King, Aditya I, established the Cholas as the main power in the Tamil Nadu region after conquering the Pallavas. Both Rajaraja Chola I and Rajendra Chola I achieved multiple naval conquests and Rajendra Chola I extended the borders of the kingdom northwards. The Cholas and Pandyas were fierce rival kingdoms until the 13th century CE.