What are the advantages and disadvantages of mixing the bypass flow with the core flow? Many Aircraft engines mix the bypass air with the core gases before exhausting to atmospheric pressure through a propelling nozzle. However, some do not mix and have separate nozzles for the flow of each. What are the advantages and disadvantages of each?

PS: I hope that I am clear now. Sorry if the question wasn't clear earlier.
In simple terms, mixing the exhaust flow (with any bypass ratio) is good for all the reasons except for construction and weight. It is aerodynamically more efficient; it reduces noise (exhaust noise makes most of the jet noise); it cools combustion chamber (and other downwind parts) more efficiently, etc.

However, making the mixing chamber on a high bypass / big engine would require enormous outer nacelle to cover the whole engine (and extend somewhat beyond), and the weight penalty and complexity/cost negates all the benefits.