The following statements are made with respect to merodiploids of the lac operon, where “I” is the lac repressor, “O” is the lac operator, “Z” is the lacZ gene encoding beta-galactosidase and “Y” is the lacY gene encoding permease:
A. In I^sO⁻Z⁺Y⁺ / I⁺O^c Z⁻Y⁺ the lacZ is inducible and lacY is constitutively expressed.
B. In I⁺O⁺Z⁺Y⁻ / I⁻O⁺Z⁻Y⁺ the lacZ and lacY are both inducible.
C. In I⁺OᶜZ⁺Y⁻ / I^s O⁺Z⁻Y⁺ the lacZ is constitutively expressed and lacY is inducible.
D. In I^s O⁺ Z⁺Y⁺ / I⁺OᶜZ⁻Y⁺ the lacZ is inducible and lacY is constitutively expressed.

Which of the following options represents the combination of all correct statements?

Correct option is A

Explanation-

I = lacI gene (lac repressor)
O = lac operator (site where the repressor binds)
Z = lacZ gene (encodes β-galactosidase)
Y = lacY gene (encodes permease)
+ = wild-type (functional)
− = mutant (non-functional)
I⁺ represses transcription normally, I⁻ cannot repress.
O⁺ allows repression by I⁺; Oᶜ (constitutive operator mutant) cannot bind repressor → genes always on, regardless of lactose presence.
Merodiploid = partially diploid bacteria with two copies of the lac operon (one on the chromosome, one on the plasmid).
Given options -
A. I⁺OᶜZ⁺Y⁺ / I⁺O⁺Z⁻Y⁺
The Oᶜ operator on the first copy makes Z⁺ constitutively expressed (always ON). I⁺ is functional but can’t bind Oᶜ, so repression fails on the first copy. Second copy has Z⁻ (non-functional), so no contribution to β-galactosidase from there.
So, lacZ is constitutively expressed, lacY is present on both — from OᶜY⁺ and O⁺Y⁺ → repressed from second copy, constitutive from first.  lacZ is constitutively expressed, lacY is also constitutively expressed.
Hence, the statement “lacZ is inducible” is incorrect.
B. I⁺O⁺Z⁺Y⁻ / I⁻OᶜZ⁻Y⁺
Chromosomal: functional repressor (I⁺), normal operator (O⁺), Z⁺, but Y⁻ → Z expressed normally only when inducer is present.
Plasmid: non-functional repressor (I⁻), Oᶜ (constitutive), Z⁻ and Y⁺
Z⁺ is under control of O⁺ and functional I⁺ → inducible
Y⁺ is under control of Oᶜ and I⁻ → constitutively expressed
lacZ is inducible, lacY is constitutive
Statement B is correct 
C. I⁺OᶜZ⁻Y⁻ / I⁻O⁺Z⁺Y⁺
Chromosomal: functional I⁺, but Z⁻Y⁻; Oᶜ (no repression).
Plasmid: non-functional I⁻, O⁺, Z⁺Y⁺
Repressor made from I⁺ on chromosome (dominant) → should control O⁺ on plasmid
But O⁺ on plasmid still binds repressor, so Z⁺ and Y⁺ are repressed unless inducer is present
OᶜZ⁻Y⁻ makes no functional protein, but Oᶜ means constitutive expression is attempted. But Z⁺ and Y⁺ on plasmid are inducible
Statement C is incorrect 
Because it says lacZ is constitutively expressed, which is false — only the Z⁻ allele is under Oᶜ.
D. I⁺O⁺Z⁺Y⁺ / I⁺OᶜZ⁻Y⁺
Chromosomal: Z⁺Y⁺ under normal control
Plasmid: Z⁻ (non-functional), Y⁺ under Oᶜ and I⁺
Z⁺ is inducible from chromosome and Y⁺ is constitutively expressed from OᶜY⁺
lacZ is inducible, lacY is constitutively expressed
Statement D is correct 

Correct Statements: B and D only
Correct Option a -  B and D only