Gujarat

You cannot do mechanical engineering degree after 10th. You are eligible for seeking admission in B.Tech after 10+2 with PCM subjects.

IRMA, IIM and NIRMA University.

Government Polytechnic Chhota Udepur
Swami Sachchidanand Polytechnic College, Visnagar
Himatnagar Polytechnic College
Government Polytechnic Gandhinagar
Government Polytechnic College
L.J. Polytechnic, Ahmedabad

It's a good university for doing management degree. As you can do MBA from that institute or you can also look for MS Patel Institute of Management.

There are many college and universities these some of them are following-
1. ITM Universe(Vadodara)
2. P P Savani University(Surat)
3. Parul University (Vadodara)
4. Samarth College of Engineering and Technology
5. Aditya Silver Oak Institute of Technology
6 .Sardar Vallabhbhai National Institute of Technology
7. Dhirubhai Ambani Institute of Information and Communication Technology

Hello Dear,
Here is a tool called college comparison app by Shiksha. You can compare any of two colleges. Here is the link:
https://www.shiksha.com/resources/college-comparison

It depends on the place where you are living.
If you are a resident of Ahmedabad, choose Nirma.