HI kindaichiXXXCertain adjectives and past participles used as adjectives can be followed by a preposition + noun / gerund. Usually specific adjectives and participles require specific prepositions. These can be found by consulting a good dictionary, which after any adjective will give the prepositions that can be used with it.PREPOSITIONS USED WITH ADJECTIVES AND PARTICIPLES
§about, at, for in, of, on to, with are the most commonly used prepositions with adjectives and participles.
There are no specific rules for which preposition to use with which adjective but learning them as you would learn a new vocabulary word seems to help most people. However, the rule for what kind of complement should follow the preposition can be deduced through the examples that accompany each adjective/preposition combination.
See the list here PREPOSITIONS USED WITH ADJECTIVES AND PARTICIPLES
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