"question the applicability" is correct and usable in written English.
You can use it when you want to express the idea of questioning the relevance of something. For example: Given the circumstances, it is important to question the applicability of the regulations.
The courts below did not question the applicability of Linn to this case.
It would be fair to question the applicability of the ATAM to commercial companies.
This alternative model calls into question the applicability of terms like "urbanism" and "the state" for early Mesopotamian society.
Rosen said the conference will question the applicability of work that dates from a very different time.
Judge Ellis's decision on the prior question, the applicability of the False Claims Act, is likely to be appealed by the losing party.
This gradual unseating of the Neptunist theory resulted from the accumulated evidence that increasingly called into question the applicability of Werner's Universal and Partial formations in describing various rock successions.
David Rind, a climate modeler and NASA scientist, has questioned the applicability of past warming episodes to the modern issue of climatic alteration caused by increased CO2 concentrations.
Neither the referee of the inquiry, nor counsel for the inquiry, nor the Appellate Division of the New York Supreme Court questioned the applicability of the privilege against self-incrimination to the records.
This finding generally questions the applicability of miRNA as robust biomarkers for discrimination.
In their 1996 monograph, Borchsenius and Bernal questioned the applicability of these subgenera.
Furthermore, "Some recent analyses have questioned the applicability of Alesina and Ardagna's findings [the findings in the 2009 study upon which Brady's JECR report had chiefly relied] to the current U.S. fiscal situation".
