When all carpels are united, they are called Gynoceium. Gynoceium is a female reproductive part of the flower however it is not directly involved in producing female gametes however it produces megaspores which develops it to gametophyte and then produce eggs.

When the carpels are free it is called?

Gynoecium having a number of free carpels is called apocarpous.

When there are more than one carpel and all the carpels are united the condition is known as?

If two or more carpels are present, they may be separate from one another (distinct), termed apocarpous, or fused together (connate), termed syncarpous.