Suitable timing for you will be depart Kota saturday moring. and reach Varanasi early morning, so that some buffer time helps both you and your son to get fresh and move to Exam center.
Preferable train Is :15635 GUWAHATI EXPRESs
date 11-5-2013 KOTA VARANASI JN
TATKAL has following quota
SL...
more... 89 berths
3A 22 berths
But that is too far off but you can give try when date comes... as a standby please try to make other arrangement too...