Apart, from JEE you should appear for BITSAT, VITEEE, SRMJEE, AEEE and

MU OET as they are the one top private colleges for engineering and provides good knowledge and excellent placements.

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

You can also check the list of entrance exams with details from the given below link

List of Engineering exams

Good luck!!