Does Red blood cells of man are alive or dead?

They still function for about 120 days after the nucleus is expelled and they become mature red blood cells. This occurs in the bone marrow before they are released into circulation. After 120 day (approx) they are no longer efficient at oxygen transport and are cleared by the liver. I would consider them "alive" in a biologically functioning way.

If the RBC are biologically function,as per cell biology living cell shoud have protoplasm(nuclues cytoplasm).

The nucleus of the RBC is expelled in the bone marrow before it is released into circulation. The purpose of the RBC is to transport oxygen to and from the tissues/organs. Immature red cells that reside in the bone marrow (and occasionally in the peripheral blood stream during illness) do have all the components of a biologically living cell.