Hi there,
Hope you are doing well.
The answer to your question would be no.
having a sixth subject in Class 11th or 12 th is not compulsory and solely a student's choice.
The school can't force any student to take a subject unwillingly.
Hope it would help.
Thank You

If you are talking about CBSE board, no sixth subject is an optional subject. You will only have 5 main subjects. 5th subject is the additional subject. You can take up a 6th subject also. If you score better in your 6th subject than your 5th, then you can consider the 6th subject for your percentage calculation. If you are confident enough in your 5th subject, then 6th subject might not be necessary for you. Other boards also have the same pattern as per my knowledge.