The correct answer is A. The Padmanabhapuram Palace was the seat of the Travancore kings. It is a palace complex located in the town of Padmanabhapuram in Kanyakumari district, Tamil Nadu, India. It was the seat of the Travancore royal family from the 16th century to the 19th century. The palace is known for its intricate woodwork and its collection of paintings, sculptures, and other artifacts.
The other options are incorrect. The Venad rulers were the rulers of the Venad kingdom, which was located in the present-day Kanyakumari district of Tamil Nadu. The Kolathiri Dynasty was a royal dynasty that ruled over the Malabar region of Kerala from the 12th to the 18th centuries. The Cochin Kingdom was a kingdom that was located in the present-day Ernakulam district of Kerala.