Thanks for A2A

Well Yes you do stand a chance of getting a seat in Lower NIT's ad IIIT's.

The best options, I can collect are

1. NIT Durgapur Bio-Tech (though chances are very narrow)

2. NIT Raipur Bio-medical (chances are again very less)

3. NIT Silchar (only when if you belong to Assam)

I personaly don't believe you can expect to have a seat at a decent NIT who holds minimum permanent faculty.

So according to me, the best possible available options are

1. Prepare well for state exams like WBJEE, UPTU and GGSIPU. Trust me, some state colleges (which these exams offer) are far better than bottom 15 NITs

2.  Prepare well for BITSAT for a month. With rigrous study for a month you can expect to have a score 300+. From this you can easily expect a seat from BITS GOA which is better than any of NIT (leaving top 5)