IIT

Yes, you can. IITs don't have any interest in the college you opted for UG. They only consider your GATE score.

Please check the college closing rank by JoSAA for IITs and NITs and compare with your rank:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx

Hi Abha,
With a score of 90% in CAT, chances for admission into FMS, Delhi look quite slim. You can always give another attempt at CAT and try to score in excess of 99% for OBC category.

Hi there, if you are getting a rank within 6000 in JEE Advanced, I'd suggest you to go for one of the old IITs, in whatever branch you get, because they offer much greater chances of all round development than other colleges. Though, if you are too inclined for a particular branch, do take it. Don't be mad about CSE, as the branch is not what you think it is. Coding can be pursued even in other branches, CSE doesn't really matter. There are always non-core placements in coding or analytics profiles in all branches. Most companies open for all branches. So prefer old IITs/NITs if you get them.

First of all, I want to congratulate them.
266 is a very good score in JEE. I think she will get a rank under 500. And with this rank, she will get top 5 IITs. And your son will get a rank under 4500. With this rank, he will get new IITs very easily.

There are many coaching institutes mainly in Kota, Delhi amd other big cities .
Bansal classes, Allen institute, Fitjee, Career point, Resonance; these are some top coaching institutes you can join.
And more than institute your hard work will determine if you crack the exam or not.
Good luck.

If you are quite specific about the branch then go for NIT. There are cases when you have interest in particular branch or subjects then don't hesitate to opt for NIT and rejecting IIT. I had to face the same situation 3 years back and i don't regret my decision at all.
Moreover, if you don't have any such particular interest then you can obviously go for IIT. It's a huge tag after all.
Be careful as it is not an easy task to go 4 years with subjects that do not interest you.
Good luck

Yes, you can, but you need to qualify JEE Mains and Advanced exam. You need to secure a rank under 2000.

No, IITs do not provide lateral entry admission. Although, many good colleges offer admission through lateral entry. SLIET Sangrur, HNBGU Uttarakhand and many more. You can take admission there.