Hey Rohit

No, Instrumentation and Control engineering is not a core branch. Their are only three core branches- Civil, Mechanical and Electrical. Although it is not properly a non core branch because in some or the other way, it has evolved from Electrical and consists of basically robotics and control and software-hardware theory(rough basis). The branch has not been that successful yet in our country, but is on its way. We still need a lot of development required.

I hope this helps. Feel free to ask any other queries.