Final answer:
In eukaryotic cells, protein-coding RNA genes are not transcribed by RNA polymerase I or III, but by RNA polymerase II.
Step-by-step explanation:
Eukaryotic cells employ three different RNA polymerases that transcribe different types of genes. RNA polymerase I transcribes ribosomal RNA (rRNA) genes, specifically the tandemly duplicated rRNA genes located in the nucleolus. RNA polymerase II is responsible for transcribing all protein-coding genes, leading to the synthesis of messenger RNA (mRNA). Lastly, RNA polymerase III transcribes RNA genes such as tRNA and small nuclear RNA genes, alongside 5S rRNA. Therefore, the answer to the given question is that protein-coding RNA genes are not transcribed by RNA polymerase I or III; they are transcribed by RNA polymerase II.