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question about noun and adjective genders

because neutral of большой is большое. Nominative case большое пиво, gen.c. большого пива, dat.c. большому пиву, acc.c. большое пиво, instrum. c. большим пивом, prepos.c. о большом пиве.

it's correct
suffixes for adjectives in nominative:
-ой for masculine
-ое for neutral
-ая for feminine

We usually don't say big beer, we prefer to say big bottle/glass/barrel of beer

As in in English, we don't use size with things, which cannot be counted. We use small portion of beer /малую порцию пива/, big bottle of beer /= большую бутылку пива/ end etc.
Do mention that russian words here are used in accusative.
And ending of adjective depends on the tare

neutral noun "большое пиво" is correct. but it's unnatural expression. we don't use it. better to say "много пива" or "большая бутылка пива"