Hello ,

No it is not possible to enroll in colleges or for JosAA counselling without giving any entrance exams. 

Your selection is based on the ranks and score you achieve in the examination. 

For engineering you need to appear for JEE MAINS AND ADVANCED LEVEL ENTRANCE EXAMS. 

For applying through JosAA counselling you need a good score in JEE MAINS. 

Hope this information was useful. Good luck.