  We study the properties of the vortex state of a trapped Bose gas in the
large-gas-parameter regime. To test validity of the Gross-Pitaevskii theory in
this regime for the vortex states we compare the results of the
Gross-Pitaevskii and the modified Gross-Pitaevskii calculations for the total
energy, the chemical potential, the density profile and the frequency shift of
the quadrupole modes of the collective oscillations of the condensate. We find
that in the large-gas-parameter regime two calculations give substantially
different results for all the properties mentioned above
