This is the 9063rd most frequent Russian word.
рузаевском
"Рузаевском" is the prepositional case form of "Рузаевский," meaning "related to Ruzaevka," a town in Russia.
'Рузаевском' describes the university in the locative case, indicating the place where the study occurs.
Он учится в Рузаевском университете.
He is studying at the Ruzaev university.
Here, 'Рузаевском' is used as an adjective describing the district, with a locative ending indicating location.
Я живу в Рузаевском районе.
I live in the Ruzaev district.
In this sentence, 'Рузаевском' functions as a descriptive adjective for the institute, again in a locative case.