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Due to recent developments on recognition issue of AMIE and such course, there is no definite answer to your question. The answer of your question was Yes before MHRD recognition withdrawal notification on 2013. Several Institutions have notified from time to time about their acceptance of AMIE as a valid eligibility or not. I will suggest you to write a mail (because I want you to have written assurance) and follow up with your query to know what is the current stand of IIT on recognition issue. While they write in their eligibility criteria :
Associate Membership Examinations recognised as equivalent to B.E. / B.Tech. Degree conducted by recognised professional bodies (like Institution of Engrs. (India), Institute of Chemical Engrs. , Aeronautical Society of India, Institute of Electronics & Telecommunication Engineers, Indian Institute of Metals etc. ).
Here the word recognised is point of consideration as for the moment there is no valid recognition and it is in discussion and pending. So to be in safe side, confirm the same with IIT once more.

Hello Matthew,
You have obtained quite good ranking in COMEDK examination. With this rank, I am sure you will get a good branch and a good college. But seeking and admission in computer sciences engineering is a different cup of tea. This is so since almost every student gives this branch as his first choice and hence cutoffs for really stiff. However, admissions are very dynamic and many times surprises do occur. Therefore, do not give up on hope. To help you I am attaching a link that can predict the branch and the college that you can get based on your ranking in this entrance examination. https://www.shiksha.com/engineering/comedk-uget-college-predictor

I had a very similar rank last year and I got NIT Rourkela foodtech engineering in around 3rd round of counselling. I dropped out of counselling in the same round so I cannot say what better things I could have got. Precisely I had a 31k rank. Also your home state plays a major role also your category. In the same rank an OBC candidate with UP home state quota got a lower branch in MNNIT Allahabad. Also as everyone states if you are from Delhi chances of getting in NSIT, DTU, IIITD will be Very high. Other than this getting a preferred branch and a good NIT would be a bit difficult but you will surely end up with a decent college if you take part in spot rounds. Do check last years cutoff ranks as they generally remain constant. By that you can judge and weigh your Options. All the best.