Arrange the following in decreasing order based on the results obtained in the ${F}_{2}$ progeny of a dihybrid cross.
(A)Total number of parental genotypes
(B)Total number of recombinant genotypes
(C)Total phenotypes
(D)Total genotypes
(a)C, B, D, A
(b)A, C, D, B
(c)D, A, C, B
(d)D, B, C, A

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Hint A dihybrid cross is a cross between two different lines or genes from the same species that differ in two observable traits. You obtain an ${F}_{1}$ generation and then an ${F}_{2}$ generation in this experiment. Each generation will produce offspring with different genotypes and phenotypes. If we follow Mendel’s three laws, we can identify the number of genotypes and phenotypes, both parental and recombinant.

Complete answer:
- In the given dihybrid cross, two individuals that differ in two observable traits are crossed with each other. The offspring form the ${F}_{1}$ generation. When this generation is self-crossed, they give rise to the ${F}_{2}$ generation that are the product of their independent occurrence.
- Say, for example, we take two parents, RRYY and rryy. The ${F}_{1}$ offspring will be all RrYy. When these plants are self-crossed, we get the following offspring:
The total number of parental genotypes: 2 (RRYY and rryy)
The total number of recombinant genotypes: 6 (RRYy, RrYY, RrYy, Rryy, rrYy, Rryy)
The total phenotypes: 4 (The phenotype is dictated by the presence of homogenous or heterogenous dominant alleles.)
The total genotypes: 9 (There are 9 non-repeating genotypes formed after the self-cross.)

Additional Information:
- In ${F}_{2}$ offspring the alleles at the two loci segregate independently.
- From the above experiment, Mendel’s law of independent assortment states that a gamete into which an r allele sorted would be equally likely to contain either a Y allele or a y allele.
- The characteristic phenotypic ratio of the ${F}_{2}$ generation is 9:3:3:1.

So, the correct answer is ‘D, B, C, A’.

Note: - Dihybrid crosses can be easily visualized by using the Punnett square.
- The three Mendelian laws are the law of segregation, the law of independent assortment, and the law of dominance.