Generally, use singular with uncountables and plural with countables, and you won't go wrong: There isn't any buckwheat paste left. There aren't any silicon wafers left. With your example, it depends on how many rules you anticipate: Are there any fixed rules?
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Mister MicawberWith your example, it depends on how many rules you anticipate:
Are there any fixed rules?
Is there any fixed rule?
Do you have any pencils?Grammatically both are correct but only the first is natural, as an inquiry into possession. Pencils are small, similar items of which we expect the listener to have several. If we wish to borrow one, we only need one-- which one is unimportant-- and will inquire, Do you have a pencil?
Do you have any pencil?