unanswerable

[uhn-an-ser-uh-buhl, -ahn-]
adjective
1.
not capable of being answered; not having a known or discoverable answer: an unanswerable question.
2.
not open to dispute or rebuttal; irrefutable; conclusive: an unanswerable proof.

Origin:
1605–15; un-1 + answerable

unanswerableness, noun
unanswerably, adverb
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World English Dictionary
unanswerable (ʌnˈɑːnsərəbəl)
 
adj
1.  incapable of being refuted
2.  (of a question) not admitting of any answer
 
un'answerableness
 
n
 
un'answerably
 
adv

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
Reflecting upon these almost unanswerable problems carries over to the rest of
  their lives.
The partner at the venture firm had asked an unanswerable question to see how
  the pair would respond.
These questions are admittedly unanswerable if one has dealt only with
  dream-symbolism.
His library was great, his reading and learning unanswerable, himself a living
  and better library.
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