The Barren island is an island located in Andaman sea, dominated by Barren Volcano, the only confirmed active volcano in South Asia. It is a part of the Indian Union Territory of Andaman and Nicobar Islands. Hence statement 1 is correct.
It lies about 135 km, northeast of the Union territory's capital Port Blair and about 540 km from Great Nicobar. Hence statement 2 is incorrect.
The volcano erupted for the first time (as per the records) in 1787. In 1991 there was another eruption that lasted for about six months and was particularly harmful to island's fauna. However there were eruptions in 1994-95 and 2005-06, the latter considered to be linked to the 2004 Indian ocean earthquake. Hence statement 3 is incorrect.