Q.What is a test cross? Explain, with a Punnett square, how a test cross can be used to determine whether a tall F1 pea plant of unknown genotype is homozygous ($TT$) or heterozygous ($Tt$) for the height gene.

A test cross is defined as crossing the F1 hybrid with the homozygous ('double') recessive genotype, to reveal the hybrid's own genotype from the resulting offspring ratio.

Working

A test cross is a specific type of cross used in genetics to determine whether an individual displaying a dominant phenotype is homozygous dominant or heterozygous, and more generally to reveal the types and proportions of gametes an individual produces. It is carried out by crossing the individual of interest -- typically the F1 hybrid, which shows the dominant phenotype but whose exact genotype is not directly visible -- with an individual that is homozygous recessive for the trait(s) concerned, i.e. carries two recessive alleles ('double recessive', for example aa for a single trait, or aabb for two traits). Since the homozygous recessive parent can only contribute recessive alleles to every offspring, the phenotype of each offspring directly reflects the particular allele combination contributed by the hybrid parent's gamete. This is precisely what option (a) describes. The other options describe different crosses: (b) and (c) describe crosses between two individuals both carrying the recessive, or both carrying the dominant, trait -- neither of these is a test cross; and (d), a cross between two F1 hybrids, is a self/F1 x F1 cross (used to obtain the F2 generation and its typical 3:1 or 9:3:3:1 ratios), not a test cross.

Crossing a dihybrid (AaBb) with a double recessive (aabb) is a test cross. AaBb makes four gamete types (AB, Ab, aB, ab) in equal frequency, aabb makes only ab, so the offspring are AaBb : Aabb : aaBb : aabb = 1 : 1 : 1 : 1.

Gametes from AaBb: AB, Ab, aB, ab (each ¼).

Gametes from aabb: only ab.

Combining each of the four gametes with ab gives:

• AB × ab → AaBb
• Ab × ab → Aabb
• aB × ab → aaBb
• ab × ab → aabb

Each in ¼ proportion → 1 : 1 : 1 : 1. This equal ratio is the signature of a dihybrid test cross, which is used to determine whether an organism showing a dominant phenotype is homozygous or heterozygous.

A frequently asked NCERT/CBSE Class 12 Biology test-cross ratio question.

A test cross of a dihybrid (RrYy x rryy) reveals the four gamete types of the heterozygote in an equal 1:1:1:1 ratio.

A test cross crosses an individual of unknown/heterozygous genotype with a homozygous recessive individual, to reveal the genotype of the gametes produced.

For a dihybrid F1 (e.g., RrYy, round-yellow), crossed with rryy (wrinkled-green):

• The heterozygote produces 4 gamete types in equal proportion: RY, Ry, rY, ry.
• Since the recessive parent contributes only recessive alleles, the offspring phenotypes directly reflect these gametes: RrYy : Rryy : rrYy : rryy = 1 : 1 : 1 : 1.

This differs from the 9:3:3:1 ratio seen in an F1 x F1 (self) dihybrid cross, which reflects the F2 generation, not a test cross.

A dihybrid test cross (AaBb x aabb) gives a 1:1:1:1 phenotypic ratio among the offspring.

Working

A test cross crosses an individual of unknown or hybrid genotype with a homozygous recessive individual to reveal the gametes it produces. For a dihybrid, the F1 double heterozygote (AaBb) produces four types of gametes in equal proportion -- AB, Ab, aB, and ab -- because the two genes assort independently (Mendel's Law of Independent Assortment). When crossed with the doubly recessive parent (aabb), which contributes only ab gametes, each of the four gamete types from the heterozygote directly produces a distinct offspring class, all in equal numbers, giving a 1:1:1:1 phenotypic ratio. This is different from a dihybrid F1 x F1 self-cross, which instead produces the well-known 9:3:3:1 ratio (option b) because both parents contribute all four gamete types. Options (a) 1:2:1 and (c) 1:1 are monohybrid ratios (self-cross and test-cross respectively), not dihybrid ratios, so they don't apply here.