A man with  B blood group marries a woman with an AB blood group. Which blood group will never appear among the progeny?

A man with B blood group can have either of the two genotypes: $I^B{I}^B$or $I^{B}i$

Woman with AB blood group has genotype: $I^A{I}^B$

Genotype of O blood group is:  i i

In order to get O blood group in progeny, both the parents must possess (i) gene. But the female mentioned in the given question does not possess (i) gene and therefore O blood group can never be seen in the progeny.