Apositively charged ball is brought close to an electrically neutral isolated conductor. the conductor is then grounded while the ball is kept close. is the conductor charged positively, charged negatively, or neutral if
(a) the ball is first taken away and then the ground connection is removed and
(b) the ground connection is first removed and then the ball is taken away?

Part a)

The conducting sphere will become neutral

Part b)

The conducting sphere will become negatively charged

Explanation:

Part a)

When ball comes closer to the conducting sphere which is Earth

Then in this case the charge appear on the near surface of the ball would be negative charge due to induction

Now if we take the ball again far away from the conducting sphere then the conducting sphere again becomes neutral as the sphere is Earthed due to which all the induced charge will flow back into the Earth

So here we will say that

if conducting sphere is Earth and the ball is taken away then in that case there is no charge on it

Part b)

Now if the ball comes close to the sphere and the Earth is removed from the sphere then in that case the charge on the sphere will be conserved as it is an isolated system now

Now if we take the ball far away from the sphere then in that case the conducting sphere becomes negatively charged and it will be uniformly distributed over its surface.