Among all the princely states during the era of British colonial rule in India, which one uniquely drafted and operated under its own distinct state constitution?

The correct option is Jammu and Kashmir.

Explanation:
During the era of British colonial rule and the subsequent integration of princely states into the Dominion/Union of India, Jammu and Kashmir occupied a unique constitutional position.
Following its accession to India in October 1947, Jammu and Kashmir was granted special autonomous status under Article 370 of the Constitution of India. Under this framework, a separate Constituent Assembly was convened for Jammu and Kashmir in 1951 to frame its own state constitution. The state constitution was formally adopted on November 17, 1956, and came into force on January 26, 1957, making Jammu and Kashmir the only former princely state in India to draft and operate under its own separate state constitution.

Analysis of Other Options:
• Travancore: Although Travancore introduced administrative and legislative reforms during the princely era, it merged with Cochin in 1949 to form Travancore-Cochin and subsequently adopted the Constitution of India.
• Mysore: Mysore was a progressive princely state with representative assemblies, but it accepted the Indian Constitution upon integration.
• Hyderabad: Hyderabad acceded to India in September 1948 after Operation Polo and was governed under the overarching framework of the Indian Constitution without creating its own distinct state constitution.