A Motor vehicle which carries passenger(s) for hire or reward and is engaged under a contract, whether expressed or implied for the use of such vehicle as a whole for the carriage of passengers mentioned therein, and entered into by a person holding a permit in relaxation of such vehicle or any person authorized by him in this behalf on a fixed or agreed rate or sum on (a) a time basis, or from one point to another, (b) and, in either case without stopping to pick up or set down passengers not included in the contract anywhere during the journey and include (c) a maxi cab and a motor cab.