out of the question vs impossible

out of the question is not a noun while impossible is a noun.

Word	Noun	Adjective	Verb	Adverb
out of the question	No	Yes	No	No
impossible	Yes	Yes	No	No

As adjectives, out of the question and impossible are synonyms defined as:

Other synonyms of out of the question include inconceivable, unimaginable.

out of the question (noun)	impossible (noun)
	something that cannot be done

out of the question (adjective)	impossible (adjective)
totally unlikely	not capable of occurring or being accomplished or dealt with
	(used of persons or their behavior) not acceptable or reasonable
	totally unlikely