IIT

Yes, it is possible to get admission in IIT without coaching (when at the time of exam your mind in genius position).

Physics- TMH Publication, IE Irodov and HC Verma.
Maths-IIT Maths by Das Gupta and TMH Publication.
Chemistry-Numerical chemistry by P Bahadur, inorganic by Pradeep Publication or Arihant and organic by Solomon and Fryle or Reso notes.

There are few good universities that accept JEE Mains scores like Thapar University, Punjab Engineering College, Delhi Technological University and NSIT.

Hello Naimish,
Here are few good colleges apart from IIT which you can join if you failed to get admission into IIT and NIT:
BITS-Pilani
IIIT-Hyderabad
Indian Institute of Space Science and Technology
Anna University
DTU, Delhi
IIIT, Allahabad
NSIT, Delhi
Jadavpur University
BIT-Mesra and Ranchi
PSG College of Technology
Institute of Chemical Technology, Mumbai
PEC University of Technology
IIEST, Shibpur
TIET, Patiala
HBTU, Kanpur
IIIT, Gwalior
College of Engineering, Pune

Hello Gautam,
BITS-Pilani, KIIT College, VIT University, PES University, Thapar University, Sastra University, Anna University, DTU Delhi, NSIT-Delhi, PGS College, BIT-Mesra and HBTU-Kanpur are best colleges apart from IIT and NIT.

Best books for maths for IIT (Mains + Advance):
TMH publication (important)
IIT mathematics (Das Gupta)
2) Chemistry
Numerical chemistry by Prakash Bahabur
Organic chemistry by resonance notes if you manage otherwise refer Solomon and Fyle
Inorganic chemistry by Arihant Publication
3) Physics
TMH publication for JEE Mains
HC Verma
4) Past years papers of MTG publication because they give it chapter wise.
5) Last moment review and revision from NCERT only.

Hi Vineet,
A candidate whose parents annual income does not exceed Rs.4,50,000/- is eligible for scholarship in IIT. So yes, you are eligible.

Hello Bharat,
The fee structure is different for different IITs. These are around Rs.70K per semester. Hostel charges are extra.