Which of the following represents a test cross in which half the offs…

The correct answer is Option (2) → Tt × tt

In a test cross, a plant with the dominant phenotype (tall, T) is crossed with the recessive parent (dwarf, tt). The offspring show which alleles the tall plant carries. Work out each cross:

Option (1) TT × tt — Incorrect. Gametes: T only × t only → all offspring Tt. Every child is heterozygous; none is homozygous recessive.

Option (2) Tt × tt — Correct. Gametes: T and t (half each) × t only → Tt : tt = 1 : 1. Half the offspring are heterozygous tall, half are homozygous recessive dwarf. This 1 : 1 result shows that the tall parent was heterozygous.

Option (3) Tt × Tt — Incorrect. This is a self-cross of two hybrids, not a test cross. Gametes T and t from both → TT : Tt : tt = 1 : 2 : 1, so only one-fourth are homozygous recessive.

Option (4) tt × tt — Incorrect. Both parents give only t → all offspring tt. There is no dominant parent to test.

NCERT Extract:
Inheritance of One Gene – “… From the preceeding paragraphs it is clear that though the genotypic ratios can be calculated using mathematical probability, by simply looking at the phenotype of a dominant trait, it is not possible to know the genotypic composition. That is, for example, whether a tall plant from F₁ or F₂ has TT or Tt composition, cannot be predicted. Therefore, to determine the genotype of a tall plant at F₂, Mendel crossed the tall plant from F₂ with a dwarf plant. This he called a test cross. In a typical test cross an organism (pea plants here) showing a dominant phenotype (and whose genotype is to be determined) is crossed with the recessive parent instead of self-crossing. The progenies of such a cross can easily be analysed to predict the genotype of the test organism.”