"The greater the acceleration the greater the _____ exerted on an object." The Correct answer would be "force."
The greater the acceleration the greater the force exerted on an object.
The question is about the relationship force = mass x acceleration. Since the question doesn't mention the mass of the object, it must remain constant. The question does indicate the acceleration increases so the only remaining variable is force. The faster a given mass accelerates the greater the force that must be exerted on it to achieve the acceleration.