The correct answer is option 1, which states that "The Barren Island volcano is an active volcano located in the Indian Territory."

Let`s break down each statement:

1. "The Barren Island volcano is an active volcano located in the Indian Territory." This statement is correct. The Barren Island volcano is the only confirmed active volcano in South Asia, and it is indeed located in the Indian Ocean, in the territory of India.

2. "Barren Island lies about 140 km east of Great Nicobar." This statement is incorrect. Barren Island is in the Andaman Sea, about 135 km northeast of the territory`s capital, Port Blair, not east of Great Nicobar.

3. "The last time the Barren Island volcano erupted was in 1991, and it has remained inactive since then." This statement is also incorrect. While it did erupt in 1991 after being dormant for over a century, it has since erupted several times, and it is still considered active.

So, only the first statement is accurate — making option 1 the correct answer.