To solve this problem, we need to identify the role of RNA polymerase III in eukaryotic transcription. Let's analyze the options:$\newline \bullet$Option 1: Transcription of tRNAs (28S, 18S and 5.8S)$\newline$ - This option is incorrect because 28S, 18S, and 5.8S rRNAs are transcribed by RNA polymerase I, not RNA polymerase III.$\newline \bullet$Option 2: Transcription of tRNA, 5S rRNA and snRNA$\newline$ - RNA polymerase III is responsible for transcribing tRNA, 5S rRNA, and some small nuclear RNAs (snRNAs).$\newline$ - This option correctly describes the role of RNA polymerase III.$\newline \bullet$Option 3: Transcription of precursor of mRNA$\newline$ - This option is incorrect because the precursor of mRNA (pre-mRNA) is transcribed by RNA polymerase II.$\newline \bullet$Option 4: Transcription of only snRNAs$\newline$ - This option is incorrect because RNA polymerase III transcribes more than just snRNAs; it also transcribes tRNA and 5S rRNA.$\newline$Therefore, the correct role of RNA polymerase III in eukaryotic transcription is described by Option 2: Transcription of tRNA, 5S rRNA and snRNA.