Can you suggest some top colleges for MBA that I can get with 81.3 percentile in CAT?

You can apply for Great Lakes, IFMR, Loyola, XIME, Christ University. I am not sure but you can apply IIT-Kanpur and IIT-Madras, as their cut-off also goes up to 80 percentile.

Hi, You can apply to all the colleges suggested but not IIT Kanpur and Madras. IIT Kanpur's official notification mentioned the cut off as 85%, just apply to and for IIT, Madras it goes around 90%. You can also try IIFM Bhopal, Welingkar Mumbai, BITS, NIT Trichy and LIBA.