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музей - Он подарил музею свою коллекцию картин. - He presented his picture (paintings) collection to the museum.
Музеям тяжело выживать в условиях капиталистического рынка – It's hard for museums to...

Well, I don't know whether it works with non-native Russian speakers but every noun case is defined by so called ruling question and the prepositions which can precisely define the case.
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