The defining characteristic of a eukaryotic cell among the options you provided is the presence of a membrane bound nucleus. Eukaryotic cells are characterized by having a nucleus that is enclosed within a nuclear membrane, which distinguishes them from prokaryotic cells, which do not have a nucleus.
While eukaryotic cells can reproduce asexually and contain DNA, the defining feature is the membrane-bound nucleus. Additionally, eukaryotic cells typically do have membrane-bound mitochondria, so that option is incorrect as well.
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