What is the location of the product of the $Lac \, y$ gene?

Statement $I$: Lac operator is present only in $lac$-operon and it interacts specifically with $lac$-repressor only.
Statement $II$: Each operon does not have a specific operator and a specific repressor.

In the given diagram of the lac operon,which one is the inducer?

Differentiation of organs and tissues in a developing organism is associated with:

In $lac$ operon,the regulator gene codes for

How is the $lac$ operon regulated by the repressor?