The correct option is B Inquisitiveness
'Inquisitiveness' means 'eager for knowledge', for example, an inquisitive person. The correct spelling lies in option B (it is the noun form of inquisitive), hence B is correct.
Options A, C and D are incorrect because they contain the incorrect spellings of the word.
('i' is missing after 'u' in A, 'e' is missing after 'v' in C and 'i' is missing after 'inquis' in D)