Statement I: "Transfer RNAs and ribosomal RNA do not interact with mRNA" is false. Both tRNA and rRNA are integral to protein synthesis, interacting with mRNA. tRNA delivers amino acids to the ribosome, and rRNA catalyzes peptide bond formation, facilitating protein synthesis.
Statement II: "RNA interference (RNAi) takes place in all eukaryotic organisms as a method of cellular defence" is true. RNAi is a process found in many eukaryotes, employing small RNAs to regulate gene expression by mRNA degradation or translation inhibition. This acts as a significant defense against viruses and transposons.
Therefore, Statement I is false, and Statement II is true.