If the blood group of the father is A and blood group of mother is B, then the blood group of the progeny could be

The correct option is B A, B, AB, O
For the above mentioned condition, the possible genotype of the blood group of the progeny would be $I^A{I}^A,I^{A}i,I^B{I}^B,I^{B}i,I^A{I}^B,\mathrm{ii}$
Hence the blood group of the progeny could be A, B, AB, or O.