Correct option is C
The correct determiner to use in the sentence "__________ friends he has are sincere" is "The few." This phrase indicates that the number of friends is small, but those he does have are sincere. The use of "The few" emphasizes the limited quantity while also acknowledging the presence of those friends.
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Meanings of all options:
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The little: Typically used with uncountable nouns to indicate a small amount, not appropriate for countable nouns like "friends."
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None: This would imply he has no friends, which contradicts the statement about their sincerity.
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Much: Used with uncountable nouns to indicate a large amount or degree, inappropriate for countable nouns like "friends."