IIT

No,Its not in IITD. Its offered in IITB with closing rank 1200. In IIT-KGP with closing rank around 3000.

Rohan there is no provision of lateral entry in IIT's so it wont be possible

I'm afraid it isn't.
JEE advanced requires concept development, but BIT SAT requires speed and accuracy along with concept development.
But preparation to JEE advanced improves your speed and concept which might help a bit in bitsat. But the difficulty level and speed in these entrance exams are way different.

It will be very difficult to crack iit jee without coaching as they teach you shortcuts for the various problems which you don't get in books. but as always people says that nothing is impossible so i suggest you to go through NCRT books deeply. try to underatand basic very clearly. solve as many questions as you can. books lyk arihant will give you good question to solve so that you can keep practising. all the best

Some of the good colleges in no particular order are:
DTU
NSIT
JAMIA MILIA
IIIT DELHI

That is a very amusing question, Harshit. It is definitely not the end of the world. Whether or not they are worth the hype, I cannot truely say. But I can certainly say that there are many colleges that give competition to some IITs, like Bits pilani, CSE at DTU and NSIT etc. NITs ofder very good career to their students by very good placements.

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For IITs Mention your board marks too.