The displacement of the object depends on the amount force acting on that object. To displace the object not only the net force but also any force can do work. So, the statement is false.
The displacement of the object at rest is. The amount of work done on that object is,
Here, is the force applied on that object, is the displacement and is the angle.
Thus, the work done on the object that is at rest is zero. So, the statement is true.
The velocity of a particle and force are perpendicular to each other. So, the particle does not move in the direction of applied force. Hence, there is no change in kinetic or potential energy of that particle. Thus, the net work done is zero.
So, the statement is true.