Explanation

'Exhausted' is an extreme (non-gradable) adjective, and extreme adjectives are intensified by 'completely', not by 'very'. 'Completely exhausted' is the idiomatic collocation, whereas 'very exhausted' is unidiomatic in standard English. 'Inordinately' and 'extremely' are possible intensifiers in other contexts, but 'completely' is the standard pairing tested here.