Introduction:
The Palk Strait is a narrow strip of water that separates the southeastern coast of India from the northern coast of Sri Lanka. It is named after Robert Palk, a former Governor of Madras. The strait is about 40 to 85 kilometers wide and approximately 64 to 137 kilometers long, making it one of the closest points between India and Sri Lanka.

Tamil Nadu:
The Indian state that is connected to Sri Lanka by the Palk Strait is Tamil Nadu. Tamil Nadu is located in the southeastern part of India and shares a maritime boundary with Sri Lanka. The Palk Strait acts as a natural border between the two regions.

Geographical features:
The Palk Strait is a significant geographical feature that separates the Bay of Bengal in the northeast from the Gulf of Mannar in the southwest. It is shallow with an average depth of about 9 to 30 meters, making it possible for people and goods to travel by boats and ferries between India and Sri Lanka.

Historical and cultural connections:
Tamil Nadu and Sri Lanka have had historical and cultural connections for centuries. The Tamil people, who primarily inhabit Tamil Nadu, also have a significant presence in Sri Lanka. The Palk Strait has facilitated the movement of people, ideas, and trade between the two regions.

Fishing and marine life:
The Palk Strait is also known for its rich marine life and fishing activities. It serves as an important fishing ground for both Indian and Sri Lankan fishermen. The strait is home to various fish species, including sardines, mackerel, and tuna.

Conclusion:
In conclusion, Tamil Nadu is the Indian state that is connected to Sri Lanka by the Palk Strait. This geographical feature has played a significant role in facilitating historical, cultural, and economic connections between the two regions. It serves as a vital waterway for trade, transportation, and fishing activities.