A test cross is carried out:

Options

A. Assess the number of alleles of a gene
B. Determine whether two species or varieties will breed successfully
C. determine the genotype of a plant at `F_(2)`
D. Predict whether two traits are linked

Answer

### Step-by-Step Solution:

1. **Understanding the Test Cross**:
A test cross is a genetic cross performed to determine the genotype of an organism that exhibits a dominant phenotype. The organism in question could either be homozygous dominant (AA) or heterozygous (Aa).

2. **Crossing with Homozygous Recessive**:
In a test cross, the organism with the dominant phenotype is crossed with a homozygous recessive organism (aa). This is crucial because the homozygous recessive organism will only contribute recessive alleles to the offspring.

3. **Analyzing the Offspring**:
The offspring (progeny) produced from this cross will reveal the genotype of the dominant phenotype parent. If all offspring display the dominant phenotype, the parent is likely homozygous dominant (AA). If there is a mix of phenotypes (both dominant and recessive), the parent is heterozygous (Aa).

4. **Conclusion**:
Thus, the primary purpose of a test cross is to determine the genotype of an organism exhibiting a dominant phenotype. In the context of the question, the correct answer is option C: "to determine the genotype of a plant at F2."