The correct answer is (a). Amaravati is a major center of Buddhism in Andhra Pradesh, India. It is famous for its Great Stupa and sculptures. The Great Stupa is a large Buddhist monument that was built in the 3rd century BCE. It is one of the most important Buddhist monuments in India. The sculptures at Amaravati are also very famous. They are made of stone and depict scenes from the life of Buddha.
Option (b) is incorrect because Amaravati is not famous for its rock-cut caves and monasteries. There are some rock-cut caves and monasteries in Amaravati, but they are not as famous as the Great Stupa and sculptures.
Option (c) is incorrect because Amaravati is not famous for its inscriptions and pilgrimage routes. There are some inscriptions and pilgrimage routes in Amaravati, but they are not as famous as the Great Stupa and sculptures.
Option (d) is incorrect because Amaravati is not famous for its university and libraries. There is no university or library in Amaravati.