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?

Let's evaluate each statement regarding Barren Island volcano:

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 has erupted multiple times in recent decades.

2. Barren Island lies about 140 km east of Great Nicobar. This statement is incorrect. Barren Island is located approximately 135-140 km northeast of Port Blair, the capital of the Andaman and Nicobar Islands. Great Nicobar is much further south (over 500 km south of Port Blair), and Barren Island is not located east of it.

3. The last time the Barren Island volcano erupted was in 1991 and it has remained inactive since then. This statement is incorrect. While it did erupt in 1991, it has erupted several times since then, including significant eruptions in 2005-06 and 2017, and subsequent minor activities. Therefore, it has not remained inactive since 1991.

Based on the analysis, only statement 1 is correct.