• 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.