The correct answer is D. Travancore.
The Kavalappara Nair family was a prominent Nair family in the erstwhile Travancore kingdom. They were known for their military prowess and played a significant role in the defense of the kingdom against foreign invaders. The family’s most famous member was Kavalappara Kottarathil Rama Varma, who was a general in the Travancore army and led the kingdom to victory in several battles.
The Kavalappara Nair family was also involved in the administration of the Travancore kingdom. They held several important positions in the government, including the post of Dewan. The family’s influence declined in the late 19th century, but they continued to play a role in the social and political life of Travancore.
The other options are incorrect. Cochin, Kozhikode, and Venad were all kingdoms in Kerala, but the Kavalappara Nair family did not play a significant role in their military or political affairs.