Hello,Mansuri

Yes there are some private colleges which do not use JEE scores for admission and are still famous and popular,they include:

BITS pilani-best private institute ,exam -BITSAT

VIT Vellore-exam VITEEE

Manipal,LPU,AMU-ALIGARH,Delhi university.

These are some of the top private institute that donot accept JEE score but do conduct their own entrance exam, which more or less has the same syllabus.So it is advisable that you can prepare for these exams while preparing for your 10+2.If you are preparing for JEE still you can sit for these exams as they are similar.5-6 months of full preparation is enough to get a seat in these top private institute.

Hope this helps you,If any further query plase do revert back.