Consider the following statements:

1. The Barren Island volcano is an active volcano located in the Indian territory.
2. Barren Island lies about 140 km east of Great Nicobar.
3. The last time the Barren Island volcano erupted was in 1991 and it has remained inactive since then.

Which of the statements given above is/are correct?

The correct option is 1 only.

Let us analyze each statement step-by-step to understand the reasoning behind this answer:

Statement 1: "The Barren Island volcano is an active volcano located in the Indian territory."
This statement is correct. Barren Island, located in the Andaman Sea, is India's only confirmed active volcano. It lies in the Andaman and Nicobar Islands region of Indian territory.

Statement 2: "Barren Island lies about 140 km east of Great Nicobar."
This statement is incorrect. Barren Island is located about 138 km (roughly 140 km) east/north-east of Port Blair (the capital of the Andaman and Nicobar Islands), not Great Nicobar.

Statement 3: "The last time the Barren Island volcano erupted was in 1991 and it has remained inactive since then."
This statement is incorrect. While the volcano did erupt in 1991 after lying dormant for about 177 years, it has experienced several major and minor eruptions since then (e.g., in 1994-95, 2005-07, and more recent sporadic volcanic activity). Therefore, it has not remained inactive since 1991.

Thus, only statement 1 is correct.