how could i use 13Cn.m.r spectroscopy to distinguish between the ketone and the alcohol?
Chemical shift of the C-OH and C=O. You can drive a bus through the difference! A C-OH is around the d60-d70 mark and C=O at about d200-d210. (acetone C=O is about d206, isopropanol C-OH is about d65).
You don't say which ketone and alcohol.