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A test cross is carried out to
A. Predict whether two traits are linked
B. Assess the number of alleles of a gene
C. Determine whether two species or varieties will breed successfully
D. Determine the genotype of a plant at \[{{F}_{2}}\]

Answer
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Hint: A test cross happens in between a double recessive parent and \[{{F}_{1}}\] generation. Moreover, it tells that if an organism is showing the dominant trait is homozygous or heterozygous.

Complete step by step answer: Gregor Mendel introduced the idea of a test cross. He introduced this technique to know that if an organism is exhibiting a dominant trait is homozygous or heterozygous.
-The physical characters or phenotype of an organism are characterized by its genetic constitution. This genetic framework of an individual is called its genotype. Thus, a test cross is simply a test to determine the genotype of an organism.
-Let us understand the test cross with the help of an example and determine what character can be identified from a test cross.
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-Consider a cross between a tall and dwarf plant with genotypes homozygous tall TT and homozygous dwarf tt. Where T represents a tall trait and t represents a dwarf trait. When they will be crossed their progeny comes out to be all tall plants as the T is a dominant trait and expresses itself whenever it will pair with t. so, this will be the \[{{F}_{1}}\] generation.
-The test cross will be done to know that the \[{{F}_{1}}\] generation obtained has a homozygous tall combination or a heterozygous tall combination. The homozygous will be TT and the heterozygous will be Tt. So, a test cross will be done between the dwarf parent plant with genotype tt and \[{{F}_{1}}\] generation plants.
-After the cross is done we will obtain the progeny that will be \[{{F}_{2}}\] progeny. Here it will be noticed that half of the progeny is tall with genotype Tt and half is dwarf with genotype tt. This means that the \[{{F}_{1}}\] generation is having a heterozygous tall genotype that is Tt.
-Therefore, after a test cross, we came to know about the type of genotype of \[{{F}_{1}}\] generation. Also, we can determine what is the genotype of \[{{F}_{2}}\] generation.
Hence, the right answer is option D. A test cross is carried out to determine the genotype of the plant at \[{{F}_{2}}\].

Note: In \[{{F}_{2}}\] generation, if all the progeny are recessive then the unknown dominant genotype will always be heterozygous. Heterozygous means a genotype having a combination of two different alleles for a single trait like Tt. In the case of all dominant phenotypes \[{{F}_{2}}\] generation, the unknown dominant will be homozygous. This means a genotype that will have double the same allele for a single trait like TT.