Final answer:
In the nucleus of a eukaryote, the processes of transcription and RNA processing occur; translation takes place in the cytoplasm.
Step-by-step explanation:
The cellular process that occurs in the nucleus of a eukaryote is transcription and RNA processing. In eukaryotic cells, DNA is transcribed into RNA within the cell's nucleus. Post transcription, the RNA undergoes several processing steps including the addition of a 5' cap, splicing of introns, and addition of a poly-A tail. While translation does occur in the cell, it is not within the nucleus but in the cytoplasm. Therefore, the correct answer to the question is E. Transcription and RNA processing.