entrance examination vs entrance exam

entrance examination and entrance exam both are nouns.

Word	Noun	Adjective	Verb	Adverb
entrance examination	Yes	No	No	No
entrance exam	Yes	No	No	No

As nouns, entrance examination and entrance exam are synonyms defined as:

entrance examination and entrance exam: examination to determine a candidate's preparation for a course of studies

entrance examination (noun)	entrance exam (noun)
examination to determine a candidate's preparation for a course of studies	examination to determine a candidate's preparation for a course of studies