Yesterday, I was on the webinar which was conducted by Manipal University, the Jee-Mains marks are invaluable to them. Their admission procedure doesn’t include any admission from Jee-Mains, but to get into them you will have to qualify their own privately conducting entrance examinations.
You have to get just 60% in board and a qualifying rank in their entrance examinations.
The exams conducted by different engg. colleages (private) :
VIT University: VITEEE
Manipal University: MU-OET
Bits Pilani: BITSAT
SRM University: SRMJEE
KIIT University: KITEEE
Amity University: AmityJEE
There are many other universities you can get into it easily.
Hope this is helpful to you.