Name the pulley which has no gain in mechanical advantage. Explain, why is such a pulley then used?

The pulley that has no gain in mechanical advantage is a single fixed pulley.

A single fixed pulley is used only to change the direction of effort to be applied i.e. with its use the effort can be applied in a more convenient direction.

It is difficult to apply the effort upwards to lift a load up directly, but it becomes easier with the help of a fixed pulley, because the effort can be applied in the downward direction to raise the load up. Further to apply the effort downwards one can conveniently make use of his own weight also for the effort.