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In the lac operon system, lac I gene codes for
(a) Inducer
(b) Repressor
(c) Promoter
(d) $\beta$-galactosidase

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Answer
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Hint: Operon is a cluster of structural genes found as a group. The lac operon is an inducible operon that utilizes lactose as an energy source and is activated when glucose is low and lactose is present. Lac I gene codes for a protein that represses or inhibits transcription of the lac operon. It does this by binding to the operator, which partially overlaps with the promoter.

Complete answer:
The lac operon encodes genes that need to acquire and process the lactose from the local environment. These are of different types: I, P, O, lac Z, lac Y, and lac A. Of this lac I gene codes for a repressor protein. Lac operon is the operon that governs the metabolic degradation of lactose. It is an inducible operon. The lac operon, functioning in E. Coli has been thoroughly investigated by Jacob and Monod. It is a small portion of the circular DNA of the bacterium. It consists of:
(i) three structural genes, which are coordinately induced in the presence of lactose
(ii) an operator gene
(iii) a promoter gene, and,
(iv) a regulator gene.
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The structural genes are Z, Y, and A. The code for the enzymes $\beta$-galactosidase, $\beta$-galactoside permease, and $\beta$-galactoside transacetylase. The genes are transcribed together from a single promoter and form a polycistronic mRNA, which directs the synthesis of the enzymes. Since these enzymes are governed by the same regulator system, they are called coordinated regulated enzymes.

Additional Information:
- Regulatory enzymes are inducible enzymes, produced only when lactose is present in the external nutrient medium. So, lactose serves as an inducer.
- It inactivates the repressor system and thereby induces the production of the entire enzyme system, necessary for lactose metabolism.
- Operator gene (O) is seen close to the first structural gene, namely Z. It interacts with a repressor protein and serves as an on and off switch for the transcription of structural genes to produce the enzymes.
So, the correct answer is '(b) Repressor'

Note:
- Allolactose is an intermediate product of lactose metabolism. It acts as an inducer of the lac operon. It is binding with lac repressor causes conformational changes in the repressor.
- Transcription by the structural gene is initiated by the promoter gene (P), located close to the operator gene. Promoter facilitates the binding of RNA polymerase and specifies where transcription should actually begin.
- Regulator gene R is located a little away from the operator gene. It regulates the functioning of the operator gene through the synthesis of a regular protein, called lac repressor.