Which of the following is required as inducer$(s)$ for the expression of $Lac$ operon?

How many operons are present in the $nif$ gene cluster of $Klebsiella$ $pneumoniae$?

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

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 $\text{mRNA}$.

Who provided the clear explanation of the $Lac$ operon?

What does '$1$' represent in the given figure?