1)Summer and Winter vacation are compulsory in our schools.
2)Summer and Winter vacations are compulsory in our schools.
Which is correct? If both are correct, what is the difference in meaning between them?
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They definitely both work. You might hear/read either.
I'm not sure I can help much with the difference in meaning. They are essentially the same.
The first, using the singular vacation rather than the plural vacations, might allow for the idea that you are talking only about this year's Summer and Winter vacation. Unlikely. Perhaps barely possible.
The second is clearly talking about any vacation, for this year or any other year.
Both the first and second are implying (which is to say, omitting) one word:
vacation is a bit repetitive and can be omitted, or so I suppose would be the proper way to think of it.
If there really is a single thing called "Summer and Winter vacation" (which I would judge to be highly unlikely), then there is no implication, no omitted word, no parallelism!