Only the sentence "I think this concert will be the band's best one yet" contains a possessive adjective.
An adjective is a word that describes a noun, which is a person, place, thing, or idea. More specifically, a possessive adjective needs to have a quality of ownership. In this sentence "band's" describes "one", which is a thing (one stands for concert). The "one" belongs to the "band", making it a possessive adjective.
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