Hello! Hope you are doing well! Firstly, congratulations for your rank in JEE Mains. There are lots of colleges which take JEE Mains marks into consideration. Though the private colleges have their college exams, they still take JEE Mains marks into consideration. For example, though KL college have their entrance exam, they will still consider your JEE Mains marks. You can know the chances of getting into the colleges through the following link which is used to predict your colleges:

" https://engineering.careers360.com/jee-main-college-predictor ".

Hope this information is useful to you. Good luck!