Eukaryotic cells are a type of cells found in organisms belonging to the domain Eukarya, which includes animals, plants, fungi, and protists. They are characterized by having a distinct nucleus, which contains the genetic material, as well as several other membrane-bound organelles.

Distinct Nucleus:
One of the defining features of eukaryotic cells is the presence of a distinct nucleus. The nucleus is a membrane-bound organelle that houses the cell's genetic material in the form of DNA. It is separated from the rest of the cell by a nuclear membrane, which helps protect and regulate the movement of substances in and out of the nucleus. This distinct nucleus allows for the efficient organization and regulation of genetic material, as well as the coordination of cellular activities.

Nucleolus:
Within the nucleus, there is a structure called the nucleolus. The nucleolus is not surrounded by a membrane and is involved in the production and assembly of ribosomes, which are responsible for protein synthesis. The nucleolus plays a crucial role in the production of ribosomal RNA (rRNA) and the assembly of ribosomal subunits.

Nuclear Membrane:
The nuclear membrane, also known as the nuclear envelope, is a double-layered membrane that surrounds the nucleus. It consists of an inner and outer membrane with a small space in between called the perinuclear space. The nuclear membrane separates the contents of the nucleus from the cytoplasm and helps regulate the movement of molecules between the nucleus and the cytoplasm. It contains nuclear pores, which allow for the selective transport of molecules such as RNA, proteins, and signaling molecules.

Conclusion:
Therefore, the correct answer is option (b), as eukaryotic cells have a distinct nucleus, nucleolus, and a nuclear membrane. These features are essential for the organization, protection, and regulation of genetic material, as well as the coordination of cellular activities.