You can appear for below entrance exams to take admission in engineering programs

JEE (Main+Advanced)- To take admission in IITs/NITs/IIITs and GFTIs you can appear in JEE Exam.

In order to be eligible for NITs you should have 75% marks in your board exam or you should be in top 20 percentile.

For SC/ST you should have 65% marks. 

If you have aggregate 60% in P/C/M you can apply for DTU and NSIT

There is relaxtion of marks for reserved category. 

It will take admission through JEE Main and counselling will be held through JAC Delhi. 

There are many private colleges as well who consider JEE Main to provide admission. You have to apply seperately for these exams. 

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

For top private colleges you can appear in BITSAT, VITEEE, SRMJEE, Manipal and Amrita.

Good Luck!!