Can a body undergo some displacement without travelling any distance? 

No, it is not possible for a body undergo some displacement without travelling any distance. 
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Can a body travel certain distance without undergoing any displacement?

Yes, the body can travel certain distance without undergoing any displacement.
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Define speed.


Speed of an object is defined as the time rate of change of position of the object in any direction. 

Speed is measured by the distance travelled by the object in unit time. 
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Can the distance travelled by a particle be negative?

No, the distance travelled by a particle cannot be negative or zero. It is always positive. 
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A particle moves from A to B along three different paths. Is the displacement along three paths different?

No, the displacement of the particle is same along different paths. 
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