Which of the following enzymes increases the permeability of the bacterial cell to lactose?

In eukaryotes,the regulation of gene expression could be exerted at $:-$
$(I)$ Transcriptional level (formation of primary transcript)
$(II)$ Processing level (regulation of splicing)
$(III)$ Transport of $\text{mRNA}$ from nucleus to the cytoplasm
$(IV)$ Translational level
Choose the correct order for given statements $:-$

Match Column-$I$ with Column-$II$:

Column-$I$	Column-$II$
$(i)$ Operator site	$(a)$ Codes for enzyme (protein)
$(ii)$ Promoter site	$(b)$ Codes for repressor
$(iii)$ Structural gene	$(c)$ Binding site for $RNA$ polymerase
$(iv)$ Regulator gene	$(d)$ Binding site for repressor

Select two correct statements from the four $(a-d)$ given below regarding the $lac$ operon.
$(A)$ Glucose or galactose may bind with the repressor gene and induce inactivity.
$(B)$ In the absence of lactose,the repressor binds with the operator region.
$(C)$ The $z$-gene codes for permease.
$(D)$ This was elucidated by Francois Jacob and Jacques Monod.
Which of the following are the correct statements?

The regulation of the $lac$ operon by a repressor is known as:

Which of the following is not produced by $E. coli$ in the lactose operon?