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Based on the JEE Main rank you obtained, the following colleges can be the good option for you.
1. Govind Ballabh Pant University of Agriculture and Technology (Computer, IT, ECE and Electrical)
2. Chandigarh College of Engineering and Technology (ECE)
3. Department of Technology, Shivaji University (Mech& Civil)
4. Rewa Engineering College (ECE& Electrical)
5. University Institute of Engineering and Technology, Chandigarh (EEE, Mech).

Based on the JEE Main rank you obtained, The following colleges can be the good option for you.
1. Madhav Institute of Technology and Science (ETE, Mech, )
2. Govind Ballabh Pant University of Agriculture and Technology (Electrical)
3. Vishwakarma Institute of Information Technology (Mech)
4. Chandigarh College of Engineering and Technology (EECE)
5. Thakur College of Engineering and Technology, Mumbai (Electronics, ETE& Civil). .

The NEET score above 500 can be good enough for getting BVPU for MBBS if belongs to general category. So yours chances are very less here.

Keeping the last year of trend in consideration, your chances for IGDTU for CSE, ECE, IT and Mechanical are high if belongs to Delhi under the asked category.
However if not belongs to Delhi, than you can get the following options.
1. Mechanical and Automation Engineering

Hello Chetna, registration in St. Xavier has been closed.