For IIT you need to qualify the JEE ADVANCED. Now the cut off for the OBC is 68.0234447-87.8950071. So you are eligible for the JEE ADVANCED.The last date for registration is 20/09/2021.

Now it would be of very less chances to get NIT's with the corresponding rank but you have good chances in the IIIT's such as :

• Indian Institute of Information Technology, Kottayam
• Indian Institute of Information Technology, Dharwad
• Indian Institute of Information Technology Design and Manufacturing Kancheepuram
• Indian Institute of Information Technology Design and Manufacturing, Jabalpur

For a more accurate prediction visit the link below:

To know more about the JEE ADVANCED cutoff visit the link below:

https://engineering.careers360.com/articles/jee-advanced-cutoff

TO know more about ME visit the link below:

https://www.careers360.com/courses/mechanical-engineering-course

I hope this answer helps. All the very best for your future endeavors!