Step 1: Concept
The Princely States were the numerous independent states in British India that existed before the country's independence in 1947. These states had their own rulers who paid tribute to the British Crown but retained internal autonomy.
Step 2: Meaning
Major Princely States refer to those states which played significant roles politically, economically, or culturally within the Indian subcontinent during the colonial era.
Step 3: Analysis
Patna: This is a city in Bihar and not a princely state. It was part of the British province of Bihar and Orissa.
Baroda: Also known as Vadodara, it was one of the prominent states ruled by the Gaekwad dynasty from 1742 to 1947.
Travancore (Cochin): These were two major princely states in southern India. They later merged to form the state of Kerala after independence.
Gwalior: Ruled by the Scindia dynasty, it was one of the largest and wealthiest princely states in central India.
Ayodhya: This is a city known for its religious significance as the birthplace of Lord Ram but not a princely state.
Step 4: Conclusion
The major Princely States from the given options are Baroda, Travancore (Cochin), and Gwalior.
Final Answer: (A)