The correct answer is Option C: Both Statement I and Statement II are correct.

Let's break down why:

Statement I: In eukaryotes there are three RNA polymerases in the nucleus in addition to the RNA polymerase found in the organelles.

This statement is correct. Eukaryotic cells possess three main nuclear RNA polymerases:

• RNA polymerase I: This polymerase is responsible for transcribing ribosomal RNA (rRNA), which is essential for protein synthesis.
• RNA polymerase II: This polymerase transcribes messenger RNA (mRNA), which carries genetic information from DNA to ribosomes for protein production. It also transcribes small nuclear RNAs (snRNAs) involved in splicing.
• RNA polymerase III: This polymerase transcribes transfer RNA (tRNA), which brings amino acids to the ribosome during translation, and other small RNAs like 5S rRNA.

In addition to these nuclear RNA polymerases, eukaryotes also have RNA polymerases in their organelles, like mitochondria and chloroplasts. These organellar RNA polymerases have different structures and functions compared to the nuclear RNA polymerases.

Statement II: All the three RNA polymerases in eukaryotic nucleus have different roles.

This statement is also correct. As explained above, each of the three nuclear RNA polymerases has a specific function:

• RNA polymerase I transcribes rRNA.
• RNA polymerase II transcribes mRNA and snRNAs.
• RNA polymerase III transcribes tRNA and other small RNAs.

Therefore, all three RNA polymerases in the eukaryotic nucleus have distinct roles in the process of gene expression. Their specialized functions ensure the proper synthesis of different types of RNA molecules essential for cellular processes.