Which one of the following statements is correct?

Let's analyze each statement:

A) Ajanta Caves lie in the gorge of Waghora river: This statement is correct. The famous Ajanta Caves, a UNESCO World Heritage site known for its ancient Buddhist rock-cut caves and murals, are carved into the side of a horseshoe-shaped cliff above the Waghora River in Maharashtra.

B) Sanchi Stupa lies in the gorge of Chambal river: This statement is incorrect. The Sanchi Stupa, a significant Buddhist monument, is located on a hilltop near Vidisha in Madhya Pradesh. It is not situated in the gorge of the Chambal River.

C) Pandu-lena Cave Shrines lie in the gorge of Narmada river: This statement is incorrect. The Pandavleni Caves (also known as Pandu-lena or Nasik Caves), a group of ancient rock-cut caves, are located near Nashik, Maharashtra. They are not in the gorge of the Narmada River.

D) Amaravati Stupa lies in the gorge of Godavari river: This statement is incorrect. The Amaravati Stupa, an important Buddhist site, is located on the right bank of the Krishna River in Guntur district, Andhra Pradesh. It is not situated in the gorge of the Godavari River.

Therefore, only statement A is correct.