An important seaport on the Tamil Nadu coast is:

Kochi
Tuticorin
Paradip
Visakhapatnam

The correct answer is: b) Tuticorin.

Tuticorin is a major seaport in the Indian state of Tamil Nadu. It is located on the southeastern coast of India, on the Gulf of Mannar. The port is well-connected to other parts of India by road, rail, and air. It is also a major hub for shipping and trade.

Kochi is a major port city in the Indian state of Kerala. It is located on the Arabian Sea coast. The port is well-connected to other parts of India by road, rail, and air. It is also a major hub for shipping and trade.

Paradip is a major port city in the Indian state of Odisha. It is located on the Bay of Bengal coast. The port is well-connected to other parts of India by road, rail, and air. It is also a major hub for shipping and trade.

Visakhapatnam is a major port city in the Indian state of Andhra Pradesh. It is located on the Bay of Bengal coast. The port is well-connected to other parts of India by road, rail, and air. It is also a major hub for shipping and trade.

However, Tuticorin is the only port among the four options that is located on the Tamil Nadu coast. Therefore, the correct answer is b) Tuticorin.