Hello Sahil,
As you have score well in board exams but if have appear in JEE Mains and Score a good percentile. You can get admission in different government colleges also. But if this also not happened you can apply for only private colleges and universities which may separately organized entrance exam for the admission in their college. Some of the best private colleges and universities in India are-
1-Vellore Institute of Technology (VIT),Vellore
2-Manipal University,Mangalore
3-Birla Institute of Technology & Science, Pilani  Hyderabad
4-SRM Institute of Science and Technology,Tamil Nadu
5-Lovely Professional University (LPU),Punjab