When a red grain variety of wheat is crossed with another white grain vartiety `F_(1)` hybrid is produced. On selfing of this `F_(1)-` hybrid, how many offsprings of `F_(2)-` generation resemble phenotypically to it's parents (let grain colour of wheat controlled by three gene pairs )

Options

A. `1//16`
B. `20//64`
C. `15//64`
D. `2//64`

Answer

To solve the problem of determining how many offspring of the F2 generation resemble phenotypically their parents when a red grain variety of wheat is crossed with a white grain variety, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Genetic Basis**:
- The grain color in wheat is controlled by three gene pairs (let's denote them as A, B, and C).
- Assume the red grain variety has the genotype: **AABBCC** (homozygous dominant for all three genes).
- Assume the white grain variety has the genotype: **aabbcc** (homozygous recessive for all three genes).

2. **Determine the F1 Generation**:
- When we cross these two varieties, the F1 generation will have the genotype: **AaBbCc** (heterozygous for all three genes).
- This means all F1 hybrids will have a red grain phenotype since the dominant alleles (A, B, and C) will express the red color.

3. **Selfing the F1 Generation**:
- When the F1 hybrids (AaBbCc) are selfed (crossed with themselves), we need to determine the genotypic ratios in the F2 generation.
- The F2 generation will result from a dihybrid cross of AaBbCc x AaBbCc.

4. **Calculate the Genotypic Ratios**:
- For each gene pair (A, B, and C), the phenotypic ratio in the F2 generation can be determined using the Punnett square.
- Each gene pair will segregate in a 1:2:1 ratio. Therefore, for three gene pairs, the total combinations can be calculated as:
- Total combinations = 2^3 = 8 (since each gene can be either dominant or recessive).

5. **Identify Parental Phenotypes**:
- The parental phenotypes are represented by the genotypes AABBCC (red) and aabbcc (white).
- The fraction of offspring that resemble the red grain parent (AABBCC) will be 1/64, and the fraction that resembles the white grain parent (aabbcc) will also be 1/64.

6. **Total Fraction of F2 Offspring Resembling Parents**:
- Therefore, the total fraction of F2 offspring that resemble either parent phenotypically is:
- 1/64 (for red) + 1/64 (for white) = 2/64 = 1/32.

### Final Answer:
The total fraction of F2 generation offspring that resemble phenotypically to their parents is **2/64** or **1/32**.

---