The Padmanabhapuram Palace is a fine example of architecture from the:

Travancore
Kolathunadu
Zamorin's Kozhikode
Cochin kingdom

The correct answer is A) Travancore.

The Padmanabhapuram Palace is a palace complex in Thiruvananthapuram, Kerala, India. It was the seat of power of the Travancore royal family from the 16th century to 1949. The palace is a fine example of Kerala architecture and is one of the most popular tourist destinations in Kerala.

The palace complex is spread over an area of 100 acres and consists of a number of buildings, including the main palace, the Lakshmi Vilas Palace, the Nalukettu, and the Art Gallery. The main palace is the largest building in the complex and is built in the traditional Kerala style. It has a number of courtyards, gardens, and pavilions. The Lakshmi Vilas Palace is a smaller palace that was built in the 19th century. It is now a museum that houses a collection of artifacts from the Travancore royal family. The Nalukettu is a traditional Kerala house that is built in the shape of a square. It has four rooms, each of which is dedicated to a different purpose. The Art Gallery houses a collection of paintings, sculptures, and other works of art from Kerala.

The Padmanabhapuram Palace is a UNESCO World Heritage Site and is one of the most popular tourist destinations in Kerala. It is a fine example of Kerala architecture and is a must-visit for anyone interested in the history and culture of Kerala.

The other options are incorrect because they are not the names of kingdoms that existed in Kerala.

Option B, Kolathunadu, was a kingdom that existed in Kerala from the 12th to the 16th centuries.

Option C, Zamorin’s Kozhikode, was a kingdom that existed in Kerala from the 14th to the 18th centuries.

Option D, Cochin kingdom, was a kingdom that existed in Kerala from the 14th to the 19th centuries.