Gene regulation governing lactose operon of E.coli that involves the lac I gene product is

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positive and inducible because it can be induced by lactose

feedback inhibition because excess of $β$ -galactosidase can switch off transcription

negative and repressible because repressor protein prevents transcription

negative and inducible because repressor protein prevents transcription.

answer is D.

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Detailed Solution

In the absence of lactose or allolactose, the repressor binds to the operator and prevents the effective binding of Repolymerize to the Lac promoter, to prevent the transcription of structural genes of poly cistron, known as z, y and a. Hence,it is referred to as negative regulation, as regulator gene product prevents the expression of structural genes.The Lac operon is inducible because it is
activated by an inducer molecule.
(1) Lac operon is negative and inducible.
(2) Excess of $β$ galactosidase itself disobediently switch off Lac operon.
(3) Positive regulation is promoted byactivator, which is also a product of
regulator gene and helps in binding of RNA polymerase at the promoter to promote transcription.

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