The switching on and off of the $lac$ operon is regulated by which of the following?

Given below are two statements:
Statement $I$: In lac operon,the repressor protein binds to the promoter region of the operon and prevents $\text{RNA}$ polymerase from transcribing the operon.
Statement $II$: Regulation of lac operon can also be visualized as regulation of enzyme synthesis by its substrate.
In the light of the above statements,choose the correct answer from the options given below:

Which of the following acts as an inducer for the $lac$ operon in $Escherichia$ $coli$?

$E. coli$ cells with a mutated $Z$ gene of the $lac$ operon cannot grow in a medium containing only lactose as the source of energy because:

What does an operon represent?

What is the first level of regulation of gene expression in eukaryotes?