Yes! You heard it right.
There are some NITs, IIITs and GFTIs whose minimum eligibility criteria for college is/are other than 75%.

Take a look at some college brochures of the list and you will find it.

If you don't believe just have a look at brochures.

BEFORE THAT !
YOU NEED TO KNOW THAT I AM ONLY INFORMING YOU ABOUT ELIGIBILITY CRITERIA OF SOME COLLEGES.

But JOSAA BUSINESS RULES are DIFFERENT...


( IT SAYS THAT IT NEEDS MINIMUM 75% MARKS IN 10+2 TO GET ADMISSION IN COLLEGES VIA JOSAA COUNSELLING SYSTEM )

So, you are really gonna need 75% in 10+2 in exam, if you are taking admission in colleges via josaa, so you have to follow its fucking business rules dude.

In short, 
"you are going to need 75% if you are taking admission in college via josaa...
and if you not taking admission via josaa then you are not but only college brochure's %age."

Now coming to the point the name of colleges are :

NIT's_
NITC Calicut (60%)
NITJ Jalandhar (60%)
VNIT Nagpur (50%)
NITR Rourkela (50%)
NIT Silchar (passed)
etc...

IIIT's_
IIITA Allahabad (60%)
IIITDMJ Jabalpur (50%)
IIITG Assam (passed)
IIITV Gujrat (50%)
IIITK Rajasthan (55%)
IIIT Lucknow (45%)
IIIT Bhopal (50%)
etc...

GFTI's_
Assam University (60%)
ITGGV or ITGGU Bilaspur (50%)
NIELIT Aurangabad (45%)
IIEST (45%)
etc...

thats all,
you will find only few more
CHECK COLLEGE BROCHURES
or if you cannot find brochures
THEN YOU CAN SEE COLLEGES ELIGIBILITY INFORMATION ON
collegedunia.com
Good Bye.
See You All Soon

ASK FOR DOUBTS !