Yes, the given statement is true. This can happen when the object returns to its original position.

For example, suppose a person walks 40m North, then 60m East, then 40m South, and finally 60m West. The person has travelled a distance of 200 m. But as he returns to his starting point, the displacement is zero.

Also, suppose you are walking around a circular park of radius 700m. You complete one round, then you have travelled the distance equal to circumference (here it is 4400 m), however your displacement is zero.

However, the reverse (converse) of this statement, which is "Distance may be zero even when the displacement is not zero" is False. If a person covers a particular distance, then the displacement is also there. If displacement is not zero, then distance can never be zero.

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It is true if the body is travelling in a closed path,i.e., if its initial and final positions are same,as displacement is the shortest distance between the initial and the final position and in this  case they are same so displacement is zero. eg. a sportsman running in a track (when he comes back to his initial position)
but the reverse is not the same bcoz distance is the length of path from the initial position to the final position and if displacement is non-zero then their is some movement so distance in this case cannot be zero  
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