The state/union territory having coast on the Bay of Bengal is :

The correct option is Andhra Pradesh.

Step-by-Step Explanation:

1. Understanding the Geography of India's Coastline:
India has a long coastline bordering the Indian Ocean, which is divided into two major water bodies on either side of the peninsula:
- The Arabian Sea to the west.
- The Bay of Bengal to the east.

2. Analyzing the Given Options:

- Karnataka: Located in southwestern India, its coast lies along the Arabian Sea (known as the Kanara/Karnataka coast).
- Kerala: Located in southwestern India, its coast (the Malabar Coast) lies along the Arabian Sea.
- Telangana: A landlocked state in southern India that does not have any coastline.
- Andhra Pradesh: Located along the southeastern coast of India, it features the second-longest coastline among Indian states, which lies along the Bay of Bengal.

3. Conclusion:
Among the given choices, Andhra Pradesh is the state that has a coast bordering the Bay of Bengal.