The correct answer is: b) Salem.
Lignite mines are primarily located in the Salem district of Tamil Nadu. The Salem district is located in the northern part of the state and is known for its rich deposits of lignite. Lignite is a type of coal that is less mature than bituminous coal and is used primarily for power generation. The Salem district is home to several lignite mines, including the Neyveli Lignite Corporation (NLC) mine. The NLC mine is the largest lignite mine in India and is a major source of power for the state of Tamil Nadu.
The other options are incorrect. Cuddalore is a district located in the southern part of Tamil Nadu and is not known for its lignite deposits. Tirunelveli is a district located in the southern part of Tamil Nadu and is known for its oil fields. Coimbatore is a district located in the western part of Tamil Nadu and is known for its textile industry.