The following pedigree chart is based on the information given in the question.
The parents don’t express the inherited trait. They have seven children (five sons and two daughters). Three of the sons suffer from the given disease but none of the daughters are affected.
Since only sons are affected, this might give us an impression that it is a Y-linked trait. But it is not a Y-linked trait as the father is not affected and two sons are also not affected. In a Y-linked trait, all the males will be affected. So, now the probability remains that it could either be an X-linked trait or an autosomal trait.
Case I:- Let us assume that it is an autosomal trait.
It is not a dominant trait. If it were so, either the mother or the father or both would have been affected. A recessive autosomal trait must be present in a homozygous condition to express itself. This means the affected sons must have received one recessive allele from each parent; it would make the both parents heterozygous. Since not all the progeny are affected (i.e. they have received dominant alleles from each parent), this could be an autosomal recessive trait. But we have not been given this option.
Case II:- Let us assume that it is an X- linked trait.
It is not a dominant trait. If it were X-linked dominant, either the father or the mother who possess the gene would have been affected. But it is not so. So, it is a recessive trait. In males, the trait can express itself in hemizygous condition, but in females, it would express only in homozygous condition. The affected sons would be hemizygous for the trait and mother would be heterozygous for the same. So, this pedigree could be a representation of the X-linked recessive trait as well. This makes option d correct.
Sex limited traits are seen in only one of the sexes. It is not seen in both sexes. Sex-limited genes are genes that are present in both sexes of sexually reproducing species but are expressed in only one sex and have no penetrance, or are simply 'turned off' in the other. This term is restricted to autosomal traits.