In a plant three dominat independently assorting gene A, B and C are essential for production of purple pigment. If any of the genes or all three genes are present in recessive condition then flower is coloures
Raw material `overset(A) to X overset(B) to T overset(C) to Z` pigment
A purple lant with genotype AABBCC crossed with a colourless plant with genotype aabbcc gibes purple `F_(1)` what proportion of coloured offspring in `F_(2)` -

Options

A. `27/64`
B. `1/64`
C. `9/64`
D. `37/64`

Answer

To solve the problem, we need to determine the proportion of colored offspring in the F2 generation when a purple plant with genotype AABBCC is crossed with a colorless plant with genotype aabbcc.

### Step-by-Step Solution:

1. **Identify the Genotypes**:
- The purple plant has the genotype AABBCC (homozygous dominant for all three genes).
- The colorless plant has the genotype aabbcc (homozygous recessive for all three genes).

2. **Crossing the Genotypes**:
- When we cross AABBCC (purple) with aabbcc (colorless), all the offspring (F1 generation) will have the genotype AaBbCc. This is because each gene contributes one allele from each parent.

3. **Determine F1 Generation**:
- The F1 generation (AaBbCc) will be purple because all three dominant alleles (A, B, and C) are present.

4. **Gamete Formation**:
- Each parent can produce gametes. The purple plant (AABBCC) can only produce one type of gamete: ABC.
- The colorless plant (aabbcc) can only produce one type of gamete: abc.
- Thus, the F1 generation can produce gametes: ABC.

5. **F2 Generation**:
- To find the F2 generation, we need to self-cross the F1 generation (AaBbCc).
- The number of different gametes produced by AaBbCc can be calculated using the formula 2^n, where n is the number of heterozygous gene pairs. Here, n = 3 (A, B, and C), so the number of gametes = 2^3 = 8.

6. **Punnett Square**:
- When we perform a dihybrid cross using a Punnett square for AaBbCc x AaBbCc, we will have 8 different gametes from each parent, leading to a total of 8 x 8 = 64 combinations.

7. **Determine the Proportion of Colored Offspring**:
- The colored offspring will be those that have at least one dominant allele for each of the three genes (A, B, and C).
- The only combinations that will result in colorless flowers are those that have at least one recessive allele in any of the three genes (e.g., aabbcc, Aabbcc, AaBbcc, etc.).
- The combinations that yield purple flowers can be calculated as follows:
- Total combinations = 64
- Combinations that are colorless = 1 (aabbcc) + combinations with at least one recessive allele in any of the three genes.
- Using the binomial expansion or counting, we find that 27 combinations will result in purple flowers.

8. **Final Calculation**:
- Therefore, the proportion of colored (purple) offspring in the F2 generation = Number of purple combinations / Total combinations = 27/64.

### Final Answer:
The proportion of colored offspring in F2 is **27/64**.