The river which flows through the Grand Canyon of India, also known as the Gandikota Gorge is

The correct option is Penna.

Step-by-Step Explanation:
1. Understanding the Gandikota Gorge:
Gandikota is a historical village situated in the Kadapa district of Andhra Pradesh, India. It is famous for a spectacular natural gorge formed by a river cutting through the Erramala hills. Due to its striking resemblance to the famous Grand Canyon in Arizona, USA, this site is widely celebrated as the "Grand Canyon of India".

2. Identifying the River:
The river responsible for carving out this breathtaking gorge is the Penna River (also known as the Pennar River). Over millions of years, the continuous flow of the Penna River eroded the bedrock of the Erramala range, sculpting the deep, narrow valley with massive walls of pink granite.

3. Analyzing other options:
- Ganga: A major river of northern and eastern India, flowing far away from the Deccan plateau region where Gandikota is located.
- Krishna: Another prominent river of southern India, but its path and basin lie north of the Penna River and do not intersect with the Gandikota range.
- Brahmaputra: A transboundary river flowing through Tibet, northeastern India (Assam and Arunachal Pradesh), and Bangladesh, located thousands of kilometers away from the gorge.