The correct option is D X – linked dominant
According to the pedigree, father is diseased and mother is normal in the first parent generation. All the daughters of first filial are diseased while sons are normal which means that daughters have inherited the disease from the diseased father; the trait is sex linked.
If it would have been an autosomal trait, the father would have transmitted the disease to the sons also. Further, since the daughters are diseased, not the sons; the trait is X-linked, not Y-linked. This is due to the fact that fathers transmit their X-chromosome daughters.
As shown the mother of first parent generation is normal, hence the daughter must have inherited only one copy of affected allele from father. This means that the trait is expressed in heterozygous condition in the daughters of first filial generation, thus the trait is dominant.
The mother of second parent generation is heterozygous dominant while father is normal. The 1/3 sons and 1/2 daughters are diseased in second filial generation.
So, correct answer is A.