Concept:
The lac operon in E.coli controls the metabolism of lactose. It is an inducible operon that becomes active in the presence of lactose.
Important components of the lac operon include:
• Regulator gene (\(lacI\))
• Promoter
• Operator
• Structural genes (\(lacZ, lacY, lacA\))
In the absence of lactose:
\[
\text{Repressor protein binds to operator}
\]
and blocks transcription.
When lactose is present, it acts as an inducer.
Step 1: Binding of lactose to repressor.
Lactose (actually allolactose) binds to the repressor protein:
\[
\boxed{B}
\]
This changes the shape of the repressor.
Step 2: Removal of repressor from operator.
After inducer binding:
\[
\text{Repressor detaches from operator}
\]
Thus:
\[
\boxed{E}
\]
Step 3: RNA polymerase binds to promoter.
With the operator unblocked:
\[
\text{RNA polymerase can bind to promoter}
\]
Thus:
\[
\boxed{C}
\]
Step 4: Transcription of structural genes.
RNA polymerase transcribes the lac structural genes:
\[
lacZ,\ lacY,\ lacA
\]
Thus:
\[
\boxed{D}
\]
Step 5: Formation of mRNA.
As transcription proceeds:
\[
\text{mRNA is formed}
\]
Thus:
\[
\boxed{A}
\]
Therefore, the correct order is:
\[
\boxed{B \rightarrow E \rightarrow C \rightarrow D \rightarrow A}
\]
Hence, the correct answer is:
\[
\boxed{(D)\ B, E, C, D, A}
\]