The correct answer is: c) Princely states with some autonomy under British paramountcy.
Feudatory states within the British Indian Empire were princely states with some autonomy under British paramountcy. This means that they were not fully independent, but they also did not have the same level of autonomy as British provinces. The British government had control over their foreign affairs and defense, but they were allowed to have their own internal governments.
Option a) is incorrect because feudatory states were not fully independent kingdoms. They were subject to British rule, even if they had some autonomy.
Option b) is incorrect because feudatory states were not directly ruled by British officials. They had their own governments, but the British government had control over their foreign affairs and defense.
Option d) is incorrect because feudatory states were not democratic republics. They were ruled by hereditary princes, not elected officials.