An object is undergoing uniform circular motion. It is doing 100 rounds/minute . After how much minimum time its average velocity will be zero?

Average velocity will become zero when you are crossing half the circle.
In this case object is having 100 rounds/ sec.
For one round time taken = (60sec/100 )
for half round , time taken = (60 / 100 ) / (2) sec
= ( 60/200) sec

= (6/20) = (3/10) = 0.3 sec