The domain that includes only organisms with a nucleus in their cells is Eukarya.

Here's why:

* Eukarya encompasses all organisms with eukaryotic cells, meaning cells that have a membrane-bound nucleus containing their DNA. This domain includes animals, plants, fungi, and protists.

* Bacteria and Archaea are both domains of prokaryotes, meaning they lack a nucleus and other membrane-bound organelles. Their DNA is located in a region called the nucleoid, but it's not enclosed within a membrane.