Question

a body can have zero avg. velocity but not zero avg. speed.

Answer 1

Average velocity is defined as the ratio of total displacement by TOTAL time taken. Average speed is the ratio of total distance by TOTAL time taken. As average velocity depends on displacement and displacement can be zero if the object returns to initial position . Where as distance can never be zero for a journey.

Example: 
A person completes one revolution in circular path. 
Distance = 2 *pi*r
Whereas displacement is zero as source and destination is same.
Hence A body can have zero average velocity but not zero average speed.