The rule is simple: much for non-count nouns, many for countable nouns: There are many things to do here. There has been a lot of trouble in the city. There is a lot of dust on the desk.
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Mister MicawberThere has been a lot of trouble in the city.1. Is the word 'trouble' here a non-count noun, that's why the singular verb 'has been' was used?