If the mother has a blood group B with a homozygous genotype and father has a blood group A of unknown genotype, then the possible blood groups of the children are:

The correct option is A AB and B
In the given question, the mother has blood group B with homozygous genotype and hence can be represented as I^B I^B.
However, the father has a blood group A with unknown genotype. Hence, he can have a homozygous (I^A I^A) or a heterozygous (I^A I^O) genotype.
- If the father is homozygous,

then the blood group of the progeny can be AB
-If the father is heterozygous,

then blood group can be AB or B.

Hence, progeny can have either AB or B as their blood group.