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Some of faculties’ research interests are interdisciplinary and diverse which are a good fit for my research interests.
I hope that the admission committee finds my background and strengths a good fit to the requirements of PhD program in Management Science and Systems.
Other than a few missing words like "the" here and there, I would say your usage of "good fit" is correct here. However, you might want to be more specific in your first sentence: how are diverse research interests a good fit for yours?
I don't think there is anything wrong with "good fit" here. As one of the definition of fit goes like this-:To be appropriate to; suit: music that fits your mood.But you could also use "apt" or "to the purpose" which sounds more formal.It should not be "are" a good fit,it should be "is" a good fit.
When regarded as a unit, collective nouns, as well as noun phrases denoting quantity, take singular verbs.( adopted from English language and usage site)
. . .
"Some of faculties research interests are diverse and interdisciplinary which is a good fit for my research interests." [Faculties research interests is taken as a unit.]
