Pick the correct statement.

a) average speed of a particle in a given time is never less than magnitude of average velocity.

B) it is possible to have a situation where

|dv/dt| is not equal to zero but d|v|/dt =0

C)the average velocity of a particle is zero in a time interval. it is possible that the instantaneous velocity is never zero in that interval.

D)the average velocity of a particle moving along a straight line is zero in a time interval. it is possible that the instantaneous velocity is never zero in that interval.

Correct statements r (a),(b),(c)

Validity statement for (a)

The average velocity is displacement /time but average speed is distance/ time. Since distance is always greater than or equal to displacement, it is evident that average speed is either equal to or greater than average velocity

Valdity staement for (b)

Situation b simplay states  that a situation should exist where the magnitutde of acceleration is not equal to 0 but velocity is 0. Such a situation is indeed possible when we accelerate a car frm rest.Initially the car is at rest but it has a positive acceleration

Valdity staement for (c) 

When a particle moves in a uniform circular motion, after completing 1 complete revolution its velocity is 0 but throughout the journey its has a certain instantaneous velocity.

Contradiction satment for (d)

If the average velocity for the particle is 0 then the displacement is essentially . For making 0 displacement either it should be at rest (no possible as instaneous velocity is never 0 acc to question)

or it should have to revesed its doirection. However if it revesed the direction or had simply deaccelerated during the motion  , it would surely reach a state when it will have 0 instaneous velocity. So it is the incorrect statement.