Hi aspirant

You may not get core branches in IITs but in NITs definately you will get.But still if you want to pursue M.Tech at IIT you may choose interdisciplinary branches which are under core branch department.

You can predict the colleges you might get with your score by visiting GATE college predictor.

https://engineering.careers360.com/gate-college-predictor

Check previous year cut off of the colleges here:

https://engineering.careers360.com/articles/gate-cutoff

Copy and paste these links in new tab to open it.

Hope this was helpful.