The correct answer is: A) Kolathunadu.
Desinganad was a collection of feudatory states owing allegiance to Kolathunadu. It was located in the present-day Malappuram district of Kerala, India. The rulers of Desinganad were known as the Desinganad Rajas. They were a branch of the Kolathunadu royal family.
The Desinganad Rajas were vassals of the Kolathunadu rulers. They were responsible for collecting taxes and maintaining law and order in their territories. They also had to provide military assistance to the Kolathunadu rulers in times of war.
The Desinganad Rajas were a powerful and influential family. They played a significant role in the history of Kerala.
Option B, Venad, is incorrect because Venad was a rival kingdom to Kolathunadu. The two kingdoms were often at war with each other.
Option C, Cochin, is incorrect because Cochin was a vassal state of Kolathunadu. The Cochin rulers were subordinate to the Kolathunadu rulers.
Option D, Kozhikode, is incorrect because Kozhikode was a vassal state of Kolathunadu. The Kozhikode rulers were subordinate to the Kolathunadu rulers.