Hello there...
There is no such condition that if your college (from where you'll graduate) should be aicte approved then only you can get into an IITs/NITs or IIITs after clearing gate.
The only thing you need to ensure that you've to maintain a good CGPA in your BTech (required to be eligible for appearing in gate exam) then after scoring a good rank in gate exam you can surely get admission into prestigious institute's like IITs/NITs etc. for higher studies.
Best of luck.
Thanks...
I hope it'll be helpful..
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