The total number of progeny obtained through dihybrid cross of Mendel is 1280 in `"F"_(2)` generation. How many are recombinants?

Options

A. 240
B. 360
C. 480
D. 720

Answer

To solve the problem, we need to determine how many progeny are recombinant from a dihybrid cross in the F2 generation, given that the total number of progeny is 1280.

### Step-by-Step Solution:

1. **Understand the Dihybrid Cross**:
A dihybrid cross involves two traits, and in Mendel's experiments, the phenotypic ratio in the F2 generation is typically 9:3:3:1. This means:
- 9 offspring show the dominant phenotype for both traits (parental type).
- 3 offspring show the dominant phenotype for the first trait and the recessive phenotype for the second trait (recombinant).
- 3 offspring show the recessive phenotype for the first trait and the dominant phenotype for the second trait (recombinant).
- 1 offspring shows the recessive phenotype for both traits (parental type).

2. **Calculate Total Progeny**:
The total number of progeny in the F2 generation is given as 1280.

3. **Identify the Recombinant Progeny**:
From the phenotypic ratio (9:3:3:1), we can see that out of the total 16 parts (9 + 3 + 3 + 1), the recombinant phenotypes (3 + 3 = 6) account for 6 parts.

4. **Set Up the Proportion**:
To find the number of recombinant progeny, we can set up the following proportion:
\[ \text{Number of Recombinants} = \left(\frac{\text{Number of Recombinants in Ratio}}{\text{Total Parts in Ratio}}\right) \times \text{Total Progeny} \]
Substituting the values:
\[ \text{Number of Recombinants} = \left(\frac{6}{16}\right) \times 1280 \]

5. **Perform the Calculation**:
- First, simplify \( \frac{6}{16} \) to \( \frac{3}{8} \).
- Now calculate:
\[ \text{Number of Recombinants} = \frac{3}{8} \times 1280 = 480 \]

6. **Conclusion**:
Therefore, the number of recombinant progeny in the F2 generation is **480**.