Which observation proves that a cell is a eukaryote?

Eukaryotic cells all have a nucleus. Eukaryotes are organisms that are multicellular, although there are some examples of single cellular eukaryotes. So eukaryotic cells can be either cell with a nucleus or a eukaryotic organism's cell.

The most important feature to judge whether it has nucleus membrane.

And for other choices, they are the common features of eukaryote and prokaryote.