As per ABO blood grouping system, the blood group of father is B⁺ , mother is A⁺ and child is O⁺ .Their respective genotype can be

A. I^Bi/I^Ai/ii                 B. IBIB/IAIA/ii

C. I^AI^B/iI^A/I^Bi          D. I^Ai/I^Bi/I^Ai

E. iI^B/iI^A/I^AI^B

Choose the most appropriate answer from the options given below :

The correct option is A only (which corresponds to genotype combination: father is I^Bi, mother is I^Ai, and child is ii).

To understand why this is the correct genotype combination, let us break down the genetics of the ABO blood grouping system:
The ABO blood group trait is controlled by a single gene (I) that has three multiple alleles:
1. I^A: Codes for blood type A antigen (dominant over allele i).
2. I^B: Codes for blood type B antigen (dominant over allele i).
3. i: Codes for no antigen, resulting in blood type O (recessive to both I^A and I^B).

Since the allele i is recessive, a person with blood group O must inherit one recessive i allele from each parent. Therefore, a child with blood group O⁺ must have the genotype:
$ii$

Since the child must receive one i allele from the father and one i allele from the mother:
- The father (blood group B⁺) must carry at least one i allele. His genotype must be heterozygous B, which is:
$I^{B}i$
- The mother (blood group A⁺) must carry at least one i allele. Her genotype must be heterozygous A, which is:
$I^{A}i$

Now we map these back to the choices given in the question:
- Father's genotype: I^Bi
- Mother's genotype: I^Ai
- Child's genotype: ii
This matches statement A (I^Bi/I^Ai/ii) exactly. Therefore, the genotype combination represented by A only is the correct answer.