The correct option is
A one X-chromosome of mother
In the given question, it has been mentioned that the couple is unaffected. It means the male and female partner both don’t show the trait of haemophilia. The genotype of the male parent is definitely XY. It cannot be X
hY, because in such a case, the male parent would be haemophilic, which is not the case here. So, the gene is not located on the X chromosome of the father.
It is not located on the Y chromosome of the father because the gene for haemophilia does not occur on this chromosome.
The mother could be either a carrier or with normal alleles. A carrier carries the recessive allele on one of her X chromosomes, but the dominant allele on the other chromosome masks the recessive one. The carrier female is phenotypically normal.
It has been mentioned in the question that half of the progeny has the haemophilic allele. This means one of the parents is carrying a trait which is not expressed phenotypically. Since the father is normal, we can say that the mother is a carrier. The gene is located on one of the X chromosomes of the mother.