Hi, This is not as simple as you wrote because there is a combined mixture of private and government colleges you can consider.
This is the order you can consider:
1. BITS, Pilani
2. College of Engineering, Trivandrum
3. Cochin University of Science and Technology
4. VIT, Vellore
5. Manipal, Karnataka

So you can consider the above order.
Good Luck.

• BITS PILANI
• VIT
• MANIPAL
• AMITY
• LPU