The correct answer is B) First boundary lubrication, followed by mixed-film lubrication, then finally full-film lubrication. This is the correct sequence because during start-up, the plain bearings will initially experience boundary lubrication, where the surfaces are in direct contact with only a thin layer of lubricant. As the speed increases, the bearing will transition to mixed-film lubrication, where both boundary and hydrodynamic effects are present. Finally, at full operational speed, the bearing will achieve full-film lubrication, where the surfaces are completely separated by a thick lubricant film. The other options are incorrect because they do not accurately reflect the typical progression of lubrication modes during the start-up and operation of plain bearings.