HELLO,

colleges accepting cat score of below 60 %tile is as follows 

• Birla Institute of Technology (BIT) ,jharkhand
• Institute of Public Enterprise  - IPE, hyderabad
• School of Management Sciences, Lucknow  - SMS , lucknow
• School of Management Sciences, Varanasi  - SMS, varanasi
• Entrepreneurship Development Institute of India  - EDI, ahmadabad

here is list of collegeswith a cutoff of 65%tile below in snap 

symboisis school of sport science (55 percentile)

Symbiosis Institute of Business Management, Hyderabad (60th percentile)

Symbiosis Institute of Health Sciences, Pune (60 th percentile)

hope this helps you !

all the best !