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We investigate the response of electrons confined in a quantum wire in the presence of intense terahertz (THz) electric field. An exact and powerful nonperturbative fundamental approach of Floquet theory is employed to solve the equation of motion for resonantly driven intersubband transitions. Several interesting features namely dynamic Stark shift, power broadening and hole-burning are observed with the variation in electric field strength. In addition, the degeneracy between several excited states is found to be removed in the presence of high electric field.