Why does a person with genotype IAIB show the blood group AB?

The correct answer is Option (2) → Co-dominance

When two different alleles of a gene are present together, one may hide the other (dominance), the two may give an in-between form (incomplete dominance), or both may show their full effect (co-dominance). The ABO blood group gene I has the alleles I^A and I^B, and each makes a different sugar on the red blood cells.

Option (1) Pleiotropy — Incorrect. Pleiotropy is when one gene affects many traits, as in phenylketonuria. Here two alleles of one gene act on a single trait, the blood group.

Option (2) Co-dominance — Correct. In co-dominance both alleles of a heterozygote are expressed. I^A makes the A sugar and I^B makes the B sugar, so the red blood cells carry both sugars and the blood group is AB.

Option (3) Recombination — Incorrect. Recombination is the formation of new combinations of genes not present in the parents, for example by crossing over. It does not explain how two alleles of one gene are both expressed.

NCERT Extract:
Co-dominance – “… ABO blood groups are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surface and the kind of sugar is controlled by the gene. The gene (I) has three alleles I^A, I^B and i. The alleles I^A and I^B produce a slightly different form of the sugar while allele i does not produce any sugar. … But when I^A and I^B are present together they both express their own types of sugars: this is because of co-dominance.”