DTU - Delhi Technological University

Overall, you need a minimum of 75% in class 12th to be eligible for counselling.

Yes, you have fair chances of getting admission in DTU at 25600 rank in general Category.
You may get EE, MECH, CIVIL, EP, ENE, BIOTECH, PCT in first round of counseling.
All the best.

You should maintain a minimum of 75% in class 12th.
Otherwise, you will not be eligible for DTU and NSIT.

No need to worry. At this rank, she will definitely get admission in DTU.
She has fair chances of getting EE, ECE, Mech, and Civil in first round of JAC counseling.

No, you can't get admission in DTU. Because, it needs minimum 75% in boards and qualifying marks in JEE Mains to get the lowest branch in DTU.
For branch like automobile engineering, you need to score atleast 100+ in JEE Mains.

Sorry to say, but with 18000 rank in OBC Category, you will not be able to fetch a seat in DTU in any of the branch.
You need to score a rank under 5000 in OBC Category to secure the lowest preferred branch in DTU.

If the given ranks are your category rank. Then, I will have to say that it is enough to get you into DTU. DTU is one of the topmost college of the country and holds a good reservation for delhiites.
If you are resident of Delhi then you can go try for it, you might get some non-core branch there. Or maybe, you will have to go for another options.

Deciding a college depends on various factors like stream you wish to take, and the place where you belong to. NIT-Trichy is one of the top most colleges in our country and is certainly the better option out of the three if you look in terms of academics and placements point, but as said, if you belong to North India, it would be easier for you to blend with DTU rather than NIT Trichy. I would say NIT-Trichy, then DTU, then NSIT.

You can choose any one because both the options are good for B.Tech, and I don't think any IIT is not good.

Hello
As you have scored really good marks and have category also you have chances to get DTU but you also have chances for good nits and GFTIs so for you to decide I'm attaching a link, there you can check the opening and closing rank for the various colleges.
Http://josaa.nic.in/result2016/result/openingclosingrank.aspx
And congratulations.
All the best.