JEE

1. Indian Institute of Technology (IIT), Delhi

2. Indian Institute of Technology (IIT), Bombay

3. Indian Institute of Technology (IIT), Madras

4. Indian Institute of Technology (IIT), Kharagpur

5. Indian Institute of Technology (IIT), Kanpur

6. Indian Institute of Technology (IIT), Roorkee

7. Birla Institute of Technology and Science (BITS), Pilani

8. National Institute of Technology (NIT), Tiruchirappalli

9. Delhi Technological University (DTU), Delhi

10. Vellore Institute of Technology (VIT), Vellore

Please note that there are many other good B.Teach colleges in India and this is not an exhaustive list.

The following colleges can be the options for pursuing B.Tech CSE.

1. IMS Engineering College, Gaziabad
2. Indore Institute of Science and technology
3. IIMT College of Engineering, Noida
4. GGIST Jabalpur 
5. College of engineering and technology, Akola 

You are eligible for IIT, just work hard in JEE Main to qualify Cut Off and in Advance to get IIT and NIT.

Yes, you can get, but write about the college name for better response. Private universities like LPU can give you the admission in B.Teach CSE. But you need to appear in LPUNEST scholarship exam. The eligibility criteria is given below. 10+2 with minimum 60% aggregate marks with Physics, Maths and English.

Admission criteria: JEE Main, LPUNEST or CUET

The following are the best private engineering colleges accepting JEE main scores.

1. TIET Patiala
2. SASTRA Thanjavur 
3. JIIT Noida
4. DA ICT Gandhinagar 
5. KIIT Bhubaneswar
6. Shiksha o anusandhan Bhubaneswar