The Paliath Achans were hereditary prime ministers of:

The correct answer is: B) Cochin.

The Paliath Achans were a family of Nair ministers who served as hereditary prime ministers of the Cochin Kingdom from the 16th century to the 19th century. They were appointed by the Cochin Rajas and were responsible for the administration of the kingdom. The Paliath Achans were a powerful and influential family and played a significant role in the history of Cochin.

The other options are incorrect:

• Option A: Venad was a kingdom in Kerala that existed from the 10th century to the 19th century. The Paliath Achans were not hereditary prime ministers of Venad.
• Option C: Kollam was a port city in Kerala that was founded in the 8th century. The Paliath Achans were not hereditary prime ministers of Kollam.
• Option D: Thekkumkur was a kingdom in Kerala that existed from the 11th century to the 18th century. The Paliath Achans were not hereditary prime ministers of Thekkumkur.