Here are some of the colleges name for Mechanical you can prefer.

IIT Bombay- JEE Advance

IIT Delhi- JEE Advance

IIT Madras- JEE Advance

IIT Roorkee- JEE Advance

NIT Surathkal- JEE Main

NIT Warangal- JEE Main

DTU- JEE Main

Netaji Subhash Institute of technology- JEE Main

For further to know about the college you can go through with given below link.

Top Engineering colleges

Good Luck!

Below are the top colleges for Mechanical Engineering

1- Indian Institute of Technology, Bombay

2- Indian Institute of Technology, Delhi

3- Indian Institute of Technology, Kharagpur

4- Indian Institute of Technology, Kanpur

5- Indian Institute of Technology, Madras

6- Birla Institute of Technology and Science

7- Indian Institute of Technology, Roorkee

8- Indian Institute of Technology, Guwahati

9- Delhi Technological University

10- Indian Institute of Technology, Varanasi

11- Anna University

12- Indian Institute of Technology (Indian School of Mines), Dhanbad

13- National Institute of Technology, Tiruchirappalli

14- National Institute of Technology, Surathkal

15- National Institute of Technology, Warangal

16- Netaji Subhas Institute of Technology

17- Indian Institute of Engineering Science and Technology

18- VIT University, Vellore

19- Birla Institute of Technology, Mesra

20- College of Engineering, Pune

Good Luck!!

You can consider below names -

Indian Institute of Technology Bombay (IIT Bombay)

Indian Institute of Technology Delhi (IIT Delhi)

Indian Institute of Technology Kanpur (IIT Kanpur)

Indian Institute of Technology Madras (IIT Madras)

Indian Institute of Technology Roorkee (IIT Roorkee)

Birla Institute of Technology and Science (BITS-Pilani)

Indian Institute of Technology - Banaras Hindu University (IIT-BHU)

Indian Institute of Technology (IIT Guwahati)

National Institute of Technology, Tiruchirappalli

Indian School of Mines (ISM)

National Institute of Technology, Surathkal

Birla Institute of Technology, Mesra

Jadavpur University (Faculty of Engineering & Technology)

Motilal Nehru National Institute of Technology

PSG College of Technology

PEC University of Technology

Malaviya National Institute of Technology

Visvesvaraya National Institute of Technology

Thapar University

Manipal Institute of Technology, Karnataka

R.V.College of Engineering etc.

Hope this helps!!!