• First- Including the IITs

Indian Institute of Science, Bangalore
IIIT Hyderabad
IIT Bombay
Indian Institute of Technology Madras
Indian Institute of Technology Delhi
IIT Kanpur
BITS Pilani
IIIT-Delhi - Indraprastha Institute of Information Technology, Delhi
IIT Guwahati
NIT Trichy

• Second- Without IITs

IIIT Hyderabad
IIIT-Delhi - Indraprastha Institute of Information Technology, Delhi
BITS Pilani
NIT Trichy
National Institute of Technology Karnataka, Surathkal
NIT WARANGAL
Delhi Technological University
Netaji Subhas Institute of Technology
Dhirubhai Ambani Institute of Information and Communication Technology
National Institute of Technology Rourkela

• Third- Private Universities

BITS Pilani
IIIT Hyderabad (Its a Public-Private Institute)
Dhirubhai Ambani Institute of Information and Communication Technology
BIT Mesra
LNMIIT, Jaipur
VIT University

Dear Aritro

Top 10 engineering colleges in India:
1) IIT Bombay
2) IIT Delhi
3) IIT Kanpur
4) IIT KGP
5)  IIT Madras
6) BITS Pilani
7) IIT Roorkie
8) NIT Trichy
9) IIT Guwahati
10) IIIT Hyderabad

If you will remove IITs then:
1) BITS Pilani
2) NIT Trichy
3) IIIT Hyderabad
4) IIIT Allahabad (They have IT)
5) DTU
6) NIT Surathkal
7) NIT Allahabad
8) BITS Goa
9) NSIT Delhi
10) BIT Mesra
Most of the above colleges will accept JEE Mains & advanced rank for giving an admission. Some will consider their repective exam scores.
All the best.