10th - 8.7 gpa 12th - 88% graduation - 65 % and expected CAT %ile - 85+ which non IIM's should I apply. please suggest me.

Hi Shiva, You can apply for elite B-schools such as

Shailesh J. Mehta School
Xavier's Labour Relations Institute, Jamshedpur
Lovely Professional University, Punjab
Department of Management Studies, IIT Delhi
Indian Institute of Foreign Trade, Delhi (own test)
Management Development Institute (MDI), Gurgaon
Bharathidasan Institute of Management (BIM), Trichy
Narsee Monjee Institute of Management Studies, Mumbai
National Institute of Industrial Engineering (NITIE), Mumbai.

• IIT Delhi
  
  
  
• IIT Madras
  
  
  
• IIT Roorkee
  
  
  
• IIT Kharagpur
  
  
  
• TAPMI Manipal
  
  
  
• Goa institute of Management
  
  
  
• National institute of bank management
  
  
  
• K J somaiya institute of Management and research Mumbai
  
  
  
• Master of finance and control

• You will need to apply separately  for all of these colleges. And there are few other private colleges which might not be good like these but still you can apply in them. Make sure before selecting any college you make a thorough analysis by going through it's study patterns, placements records and reviews.

• All the best!!