Source : Webster's Revised Unabridged Dictionary (1913)

Inapplicability \In*ap`pli*ca*bil"i*ty\, n. [Cf. F.
   inapplicabilit['e].]
   The quality of being inapplicable; unfitness;
   inapplicableness.

Source : WordNet®

inapplicability
     n : irrelevance by virtue of being inapplicable to the matter at
         hand [ant: {applicability}]