For the following sentences, are they same in meaning?
1: Are you a native Chinese?
2: Are you native Chinese?
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First of all, when the name is ended with "-ese" like Chinese and Japanese, it's quite rude to use it as a noun, I prefer Chinese person or Chinese people.
You can be plural or singular(Some dialects use y'all for the plural form). I guess that puts you in a confusion. The former uses you as a singular pronoun, and the latter uses you as plural pronoun.
Are you a native Chinese? is a question for a second person.
Are you native Chinese? is a question for second persons. It may refer to a group of people
Both sentences are different in meaning.
The word Chinese is a singular noun in the former and a plural noun in the latter,
The word native is an adjective modifying the Chinese in these sentences. So these sentences mean:
Are you a native Chinese? = Are you a native of China?
Are you native Chinese? = Are you natives of China?