No there won't be any problem until and unless you are applying for the course which you have failed in, i.e if you have failed in Biology (PCMB) then you can't apply for MBBS.

Coming to the CAT issue, let me tell that for the initial Calling in IIM L only 20% weightage is given to class 12th and Graduation remaining 80 is divided between CAT score(65%) and 15% (Work Exp.).

FMS Delhi gives CAT score a weightage of 95% or sometimes 100%