IIT

It totally depends on following:
1. Cut off of colleges.
That mostly depends on number of students giving exam.
2. Seat available in colleges
3. If you have any quota, e.g.-handicap, sportsmen etc.

NPTEL is the best website for free IIT lectures. It provides good quality of content/notes from IIT.

For entering into the IITs, you need to qualify two the toughest examination I. e. JEE Mains and JEE Advanced. And for cracking these two exams, you need some best study strategies:
1. Understand each topic clearly.
2. Do lots of hardwork and practice more and more questions.
3. Make smart and good notes.
4. Revise all the formulaes.
5. Solve as many as previous year question papers.

Both of them are good but in my opinion IITs are better than BITS.

You can check this year's category wise opening and closing ranks of IITs, NITs and IIITs at:
https://josaa.nic.in/webinfocms/Handler/FileHandler.ashx?i=File&ii=139&iii=Y

Hi Sagun,
Please follow the link for a good answer.
https://ask.shiksha.com/how-to-prepare-for-iit-entrance-exam-qna-3667033

Hi Nishant, A national level examination, GATE (Graduate Aptitude Test in Engineering) is a qualifying exam for admissions to post-graduate programs (e. g. , M.E. /M.Tech direct Ph.D. in Indian institutes of higher education with financial assistance provided by MHRD and other government agencies. GATE scores may also be used in public and private sector. https://www.shiksha.com/engineering/exams/gate.

First of all, mention your category.

Yes, you are definitely eligible for IIT and need to go for the counselling.

You can visit Kakadeo for the best coaching centre. Some options are:
KalraShukla, Akash and Ashish Vishnoi.