If a cell of an organism contains a nucleus the organism is a eukaryote?
Yes. If a cell has a nucleus then it is eukaryotic and if it has no true nucleus then it a prokaryotic cell.
A eukaryote is an organism that has cells containing a membrane bound nucleus that has genetic material inside. The eukaryotic cell also contains specialized organelles that assist with proper cell divisions, energy, and membrane permeability. The complete opposite of a eukaryote is a prokaryote which consists of bacteria, etc.
eukaryote cell A single-celled or multicellular organism whose cells contain a distinct membrane-bound nucleus. prokaryote cell An organism of the kingdom Prokaryotae, constituting the bacteria and cyanobacteria, characterized by the absence of a nuclear membrane and by DNA that is not organized into chromosomes.