Which gene produces the lactose repressor?

Two scientists were awarded the Nobel Prize in $2006$ for $RNA$ interference. On which organism did these scientists discover this mechanism?

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

Which of the following statements concerning the regulatory gene $(i)$,associated with the $lac$ operon are incorrect?
$(I.)$ $\text{mRNA}$ is transcribed from the $i$ gene whether lactose is present or not.
$(II.)$ $\text{mRNA}$ is transcribed from the $i$ gene only when the lactose is present.
$(III.)$ $\text{mRNA}$ is transcribed from the $i$ gene only when the lactose is not present.
$(IV.)$ Lactose inhibits the translation of $i$ gene $\text{mRNA}$.

What effect would you expect if gene expression of the $lac$ operon were completely repressed?

The activity of structural genes is controlled by.....