incompetent vs unqualified

incompetent is a noun but unqualified is not a noun.

Word	Noun	Adjective	Verb	Adverb
incompetent	Yes	Yes	No	No
unqualified	No	Yes	No	No

As adjectives, incompetent and unqualified are synonyms defined as:

incompetent (noun)	unqualified (noun)
someone who is not competent to take effective action

incompetent (adjective)	unqualified (adjective)
not qualified or suited for a purpose	not meeting the proper standards and requirements and training
legally not qualified or sufficient	not limited or restricted
not doing a good job	legally not qualified or sufficient
not meeting requirements	having no right or entitlement
showing lack of skill or aptitude