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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How does the displacement of a particle change, when reference point for the position is shifted?

The displacement of the particle will not change because, displacement of a particle is independent of choice of reference point. 
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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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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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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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