The Balipara Frontier Tract included territories that were under the nominal control of:

Ahom kings
Tibetan rulers
Mughal Empire
British East India Company

The correct answer is: a) Ahom kings.

The Balipara Frontier Tract was a British administrative unit in the eastern Himalayas, which existed from 1874 to 1947. It was located in the present-day Indian state of Assam. The tract was originally under the control of the Ahom kings, who were a powerful Hindu dynasty that ruled over Assam from the 13th to the 18th centuries. In the 18th century, the Ahom kingdom was weakened by a series of wars with the Mughal Empire. In 1794, the Ahom king Gaurinath Singha signed a treaty with the British East India Company, which gave the British control over the Balipara Frontier Tract. The tract remained under British control until 1947, when it was merged with the Indian state of Assam.

The other options are incorrect. Option b) is incorrect because the Tibetan rulers did not have control over the Balipara Frontier Tract. Option c) is incorrect because the Mughal Empire did not have control over the Balipara Frontier Tract. Option d) is incorrect because the British East India Company did have control over the Balipara Frontier Tract, but only after 1794.