(1) Which is a road roller, tractor crane, truck crane, power shovel, road building machine, snow plow, road sweeper, sand spreader or well driller.

(2) Which is described in section five hundred four of this chapter, except subdivision four of such section.

(b) Omnibus carriers. (1) An omnibus carrier shall not be required to apply for a license and decal or decals for a qualified motor vehicle which is an omnibus operated on a public highway in this state; except, if the commissioner enters into a cooperative agreement under subdivision (b) of section five hundred twenty-eight of this article, the commissioner may, pursuant to such agreement, require such a carrier to be licensed and obtain such decal or decals with respect to such a vehicle.

(2) The taxes imposed by this article shall not apply to motor fuel and diesel motor fuel used by an omnibus carrier in the operation of an omnibus in local transit service in this state, as described under paragraph (d) of subdivision three of section two hundred eighty-nine-c of this chapter, pursuant to a certificate of public convenience and necessity issued by the commissioner of transportation of this state or by the interstate commerce commission of the United States or pursuant to a contract, franchise or consent between such carrier and a city having a population of more than one million inhabitants, or any agency of such city.

(c) Effect of cooperative agreement. Notwithstanding subdivisions (a) and (b) of this section, in the event that the commissioner enters into a cooperative agreement under subdivision (b) of section five hundred twenty-eight of this article, the commissioner may issue a license and decal or decals with respect to qualified motor vehicles described in subdivisions (a) and (b) of this section which are based in this state for the purpose of reporting and payment of tax imposed by other member jurisdictions with respect to such qualified motor vehicles.