(B) No,the distance travelled by the object would not necessarily be zero.
Displacement is a vector quantity defined as the shortest distance between the initial and final positions,whereas distance is a scalar quantity representing the total path length covered by the object.
Displacement becomes zero when an object returns to its starting point (initial position = final position) after completing a journey.
However,the object has still covered a path to return to the start,meaning the total distance travelled is greater than zero.
For example,if an athlete runs one complete lap around a circular track,their displacement is $0$,but the distance travelled is equal to the circumference of the track $(2 \pi r)$.