Mr. Kapoor has Bb autosomal gene pair and d allele sex-linked. What shall be the proportion of Bd in his sperms?

The correct option is B 1/4
Mr. Kapoor has Bb autosomal gene pair and d allele is sex-linked. The d allele would be present on either the X chromosome or the Y chromosome. So, the genotype of Mr. Kapoor would be BbX${}^d$Y or BbXY${}^d$.
According to the law of segregation, during gamete formation (meiosis), the alleles would be segregated independently into the gametes.
The probability of the sperms to be Bd would be the product of the individual probabilities of the segregation of alleles of each gene.
The probability of B (out of B and b) is ½.
The probability of d is ½ (since either the X or Y chromosome would be inherited into a sperm).
The probability of Bd would be ½ X ½ = ¼.