If you're talking about one particular examination which will take place on Monday and on no other day, then "The examination will take place on Monday". You wouldn't use "commence" here. It will commence at a particular time, perhaps. "The examination will commence at 09:00 on Monday".
If you're talking about an examination which will be taken by several people over the course of, for example a week, then you might say "The law exams will commence on Monday and continue until Friday".