You can appear in JEE Main to take admission in government colleges like DTU and NSIT it consider JEE Main marks to provide admission and counselling is held through JAC Delhi. To be eligible you must have 60% aggregate marks or more in Physics, Chemistry and Mathematics in your 12th class. There is relaxation of marks for reserved category.

Through JEE Main you can also take admission in private colleges of various states.

To check the list of private colleges you can refer below link

Top Private colleges through JEE Main

You should also appear in your state level entrance exam to take admission in government state colleges.

There are also some private entrance exam which you can appear to take admission in top private colleges of engineering

1- VITEEE

2- SRMJEE

3- Manipal

4- Amrita

5- COMEDK

Good Luck!!