Final answer:
The correct ranking of tensions is from highest to lowest: tension in the cord between the heavier box and the force, tension in the cord between the two boxes, and tension in the cord between the lighter box and the force.
Step-by-step explanation:
When two boxes are connected by a massless cord on a frictionless surface and pulled by a constant force, we can determine the tensions in the cords using Newton's laws of motion. Since the surface is frictionless and the cord is massless, we can assume that the tension is the same throughout the rope, based on Newton's third law. However, as the tension transmits the applied force through the system, the tension directly before the mass being pulled by the external force (the lighter box in this case) will be the least, because it has to pull only the mass of the lighter box. The tension between the two boxes (c) will be higher, as it has to pull both boxes. Finally, the tension in the cord between the heavier box and the force (a) will be the highest, as it has to transmit the force necessary to move both masses.