Hi
I do not think u can apply for the state colleges in Krnataka, from ur AIEEE rank as u are from Delhi and the AIEEE rank seats are reserved for the respective states. But u can still try out for other colleges which take in other students and does not require u being a resident of Karnataka.
Here is the list of some of the colleges in bangalore. u can try out for the paid seat availability as i suppose some of these colleges do have paid seats.

    

        

            

            
Engineering Colleges In Bangalore
            
        
        

            
Name & Address
            
Activity
            
 
            
Course offered
        
        

            
Acharya Institute of Technology Soldevanhalli, Hesarghatta Road, Bangalore 560090
            
Engineering
            
 
            
B.E. Courses:                     Biotech, CSE, IT, ECE, ME.
        
        

            
Atria Institute of Technology              Anandnagar, ASKB Ground, Ist Main AGS Colony,                        

            Bangalore-24
            
Engineering
            
 
            
B.E. Courses:                         Computer Science, Electronics and Comm. Telecommunication
        
        

            
B. M. S. College of Engineering P.B. No. 1908, Bull Temple Road, Bangalore 560019
            
Engineering
            
 
            
B.E. Courses:                       

            Civil (50), Chemical (40), Electrical & Electronics, Ind. Engg. & Mgt.(60), C.S. (60), 

            Mech. (100), Medical Electronics (30), Transporation (40), Manafacturing Eng. (30), Printing Tech. (60)
        
        

            
Bangalore College of Engineering and Technology    Near Heelalige Railway Station, Chandapur, Hosur Road, Bangalore
            
Engineering
            
 
            
B.E. Courses: Mechnical Engg., Electronics & Comm. Engg., Civil Engg., Computer Science, Electrical & Electronics Engg., IT & M.C.A.
        
        

            
Bangalore Institute of Technology                                          

            KR Road, Visveswarapuram, 

            Bangalore 04
            
Engineering
            
 
            
B.E. Courses: Electronics (70), Civil (90), Computer Science (70), Electrical (60), Instrumentation & Electronics, Industrial Engg. & Mgmt. (40), Mechnical (120), Telecommunication (30)
        
        

            
Bangalore Technical Foundation Trust                                             

            292, 7th Cross Road, Ist Block Jaya Nagar,    Bangalore-01
            
Engineering
            
 
            
B.E. Courses:                    Computer Science (40), Electronics & Comm., Mech.(60)
        
        

            
Dairy Science College

            Hebbal, Bangalore-24
            
Engineering
            
 
            
B.Tech. Courses:                  Dairy Tech. (25)
        
        

            
Dr. Ambedkar Institute of Technology

            Near Janana Bharati Campus, Bangalore-56
            
Engineering
            
 
            
B.E. Courses:                           

            Civil (85), Mech. (96), Computer Science(64), Electrical (53), Electronics (32), Information Sc. & Engg. (32), 

            Tele. Comm. (32)
        
        

            
Ghousia College of Engineering 

            Bangalore Mysore Road, Ramanagaram, Bangalore
            
Engineering
            
 
            
B.E. Courses:                     

            Civil Engg., Electronics Engg., Information Tech. Electrical Engg. , Mech.
        
        

            
Govt. S.K.S.J. Technological Institute

            K. R. Circle Bangalore-01
            
Engineering
            
 
            
B.Tech. Courses:                  Textile (50), 

            Silk (20),