$A$ low level of expression of lac operon occurs at all the time. Can you explain the logic behind this phenomenon?

The accessibility of promoter regions of bacterial $DNA$ in many cases is regulated by the interaction of proteins with sequences termed:

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:

Match the following genes of the $Lac$ operon with their respective products.

$(a)\; i$ gene	$(i)\; \beta-\text{galactosidase}$
$(b)\; z$ gene	$(ii)\; \text{Permease}$
$(c)\; a$ gene	$(iii)\; \text{Repressor}$
$(d)\; y$ gene	$(iv)\; \text{Transacetylase}$

Select the correct option.

The functional complex that consists of a cluster of genes including structural genes,a promoter gene,an operator gene,and a regulator gene was discovered by:

When do bacteria $NOT$ produce $\beta$-galactosidase?