The correct answer is option 'b' - Airport Authority of India.

The body managing Indian airports is the Airport Authority of India (AAI). Let's examine in detail why this is the correct answer.

1. Introduction to the Airport Authority of India (AAI)
The Airport Authority of India (AAI) is a statutory body that manages the operations and development of airports in India. It was formed on 1st April 1995 by merging the International Airports Authority of India (IAAI) and the National Airports Authority (NAA). The AAI is responsible for ensuring the safe and efficient management of Indian airports and for promoting the development of civil aviation infrastructure in the country.

2. Functions and Responsibilities of the AAI
The AAI has several key functions and responsibilities, including:

- Airport Management: The AAI manages a total of 137 airports across India, including domestic and international airports. It oversees all aspects of airport operations, including air traffic management, terminal management, ground handling, and security.

- Infrastructure Development: The AAI is responsible for the development and maintenance of airport infrastructure in India. This includes the construction of new airports, expansion and modernization of existing airports, and the development of associated facilities such as runways, terminals, and cargo handling facilities.

- Air Traffic Control: The AAI operates the air traffic control (ATC) services at all airports in India. It ensures the safe and efficient movement of aircraft within Indian airspace and provides vital communication and navigation services to pilots.

- Aviation Safety: The AAI plays a crucial role in ensuring aviation safety in India. It implements and enforces safety regulations, conducts safety audits, and provides training to airport personnel and air traffic controllers.

- Promoting Civil Aviation: The AAI promotes the growth of civil aviation in India by providing support and incentives to airlines, encouraging the development of regional connectivity, and attracting investments in airport infrastructure.

3. Conclusion
In conclusion, the Airport Authority of India (AAI) is the body responsible for managing Indian airports. It plays a vital role in ensuring the safe and efficient operation of airports, developing airport infrastructure, and promoting civil aviation in the country.