JEE Main

Yes, it is possible but you won't get very good colleges, you can also give private colleges entrances. Some colleges also give direct admission based on 12th score as well. Even some colleges are there where you can apply and they will definitely give admission. But, JEE is the prestigious exam to enter into the reputed colleges.
All the best.

JoSAA is only for government colleges and not private colleges. You have to apply for private engineering colleges separately. Many of the private colleges accept admission on the basis of JEE Mains but you have to apply separately.

JEE Advanced is specifically conducted by the IITs to admit students.

You should be in top 5 thousand rank for getting admission in dtu and nsit if you belong from outside delhi.
It means you have to score more than 240 marks.

Hello Akshat,
Chandigarh University
Thapar University
LPU
are some of the best colleges there.

Hello Arjun, congratulations for your achievement. I am assuming you to be of General category. I cannot assure you. There is a big competition for CS branch, there is 90% chance that you will get it.
All the very best.

The questions are in MCQ format and the syllabus is your 11 and 12 of CBSE board. There are some theory and some numerical of different difficulty level. You can visit this link for a better idea of the pattern.