A motor vehicle tax is imposed on motor vehicles registered for operation upon the highways of this state, except:

(1) Motor vehicles exempt from the registration fee in section 60-3,160;

(2) One motor vehicle owned and used for his or her personal transportation by a disabled or blind veteran of the United States Armed Forces as defined in section 77-202.23 whose disability or blindness is recognized by the United States Department of Veterans Affairs and who was discharged or otherwise separated with a characterization of honorable if an application for the exemption has been approved under subsection (1) of section 60-3,189;

(3) Motor vehicles owned by Indians who are members of an Indian tribe;

(4) Motor vehicles owned by a member of the United States Armed Forces serving in this state in compliance with military or naval orders or his or her spouse if such servicemember or spouse is a resident of a state other than Nebraska;

(5) Motor vehicles owned by the state and its governmental subdivisions and exempt as provided in subdivision (1)(a) or (b) of section 77-202;

(6) Motor vehicles owned and used exclusively by an organization or society qualified for a tax exemption provided in subdivision (1)(c) or (d) of section 77-202 if an application for the exemption provided in this subdivision has been approved under subsection (2) of section 60-3,189; and

(7) Trucks, trailers, or combinations thereof registered under section 60-3,198.