Why do you want to opt for engineering? Is it because you enjoy Physics, Chemistry and Mathematics? If that’s the reason, then there are two possibilities for you.
Joining IIIT Sri City for CSE-
Joining Chemical Engineering at MANIT Bhopal-
If you have no particular inclination, then choosing CSE may be better. As it has two domains, i.e. coding and non-coding. Plus, the internet is full of great ebooks and tutorials to teach you.
Having friends studying in both the institutes, I can say that MANIT Bhopal and NIT both are good in every criterion. When it comes to choosing between colleges and courses, the first preference should be given to the course you want to study.
In the given choices CSE has better growth and demand than Mechanical and NIT is slightly better than MANIT Bhopal. So the clear choice here will be CSE at NIT unless you wish to study mechanical then the other is fine too. Choose a college that is good which includes not just the NIT tag but also about management, faculty, students.