GATE 2024 BT Q.51: solution and answer

Official answer: A, DSource: Official answer key, GATE 2024 BT (IISc Bengaluru)

1. Recall lac operon dual control: negative control by the LacI repressor (operator-blocking, relieved by an inducer) and positive control by the CAP (catabolite activator protein)-cAMP complex (promoter-assisting, active when glucose is scarce).

2. Option (D) Presence of lactose: allolactose (derived from lactose) binds the LacI repressor, changing its conformation so it releases the operator — this de-represses the operon and permits transcription of lacZYA (β-galactosidase). This condition induces expression, so D is CORRECT.

3. Option (B) Absence of lactose: with no inducer present, LacI stays bound to the operator and blocks RNA polymerase from transcribing the operon — expression stays OFF. This is the opposite of induction, so B is WRONG.

4. Option (A) Absence of glucose: low/absent glucose raises intracellular cAMP; cAMP binds CAP, and the CAP-cAMP complex binds the CAP site just upstream of the lac promoter, recruiting and stabilizing RNA polymerase there (positive control). This condition strongly enhances/permits full induced expression, so A is CORRECT.

5. Option (C) Presence of glucose: high glucose lowers cAMP levels (catabolite repression), so CAP-cAMP cannot activate the promoter, and transcription stays low even when lactose (and hence de-repression) is present. So C is WRONG.

6. Since the question (an MSQ) asks generally which conditions induce/support β-galactosidase expression, both the repressor-relief condition (lactose present) and the activator-enabling condition (glucose absent) are valid, independent contributors to induced expression.

7. Final: (A) and (D) induce/support expression; (B) and (C) keep it repressed.