Should I attend NIT, Durgapur; IIITM, Gwalior; IIIT, Amethi; or drop for IIT next year?

My brother was in a similar situation back in 2014 with a rank of 11,000 in JEE advanced and 28,000 in JEE Mains. If you belong to the general category with this score, there is no chance of being able to attend IIT counseling.

• If you are determined to attend IIT, you should consider taking a drop and try again next year and not regret your decision of not getting into core IITs. 
• IIITM Gwalior or IIIT Amethi are not that great when it comes to placements.
• You will also notice that core IITs have a different vibe to them and the environment is definitely much better too. So you should definitely not settle for something less than what you deserve.
• If you think you need help preparing, you can even think of joining a coaching center. With determination and hard work, you will definitely be able to join one of the core IITs and your life will be set later.

However, ensure that you are completely sure of your decision. If you want to be on the safer side, you can take admission to IIITM Gwalior. If you are interested in coding, you will surely do well here. On the other hand, you can also prepare for JEE side by side as it is easy to be a student at IIITM Gwalior without much pressure.

In case you do succeed, you will end up at a much better institute and if not, you can always fall back on IIITM Gwalior.