In a plant species, tall plant (T) characteristic is dominant over dwarf plant (t) and violet flower characteristic (V) is dominant over white flower (v). A homozygous plant which is tall and bears violet flowers is crossed with a dwarf plant bearing white flowers. The `F_(1)`, off springs are self-crossed to produce F2 generation. If a total of 176 off springs are produced, how many plants are expected to be dwarf and bearing white flowers in `F_(2)`, generation, according to a typical Mendelian cross?

Options

A. 11
B. 26
C. 33
D. 99

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the Genotypes of the Parent Plants
- The homozygous tall plant with violet flowers has the genotype **TTVV**.
- The dwarf plant with white flowers has the genotype **ttvv**.

### Step 2: Determine the Genotypes of the F1 Generation
- When we cross TT (tall) with tt (dwarf) and VV (violet) with vv (white), all offspring in the F1 generation will inherit one allele from each parent.
- The F1 genotype will be **TtVv** (tall with violet flowers).

### Step 3: Self-Cross the F1 Generation
- The F1 plants (TtVv) are then self-crossed. This means we will perform a dihybrid cross.
- The gametes produced by TtVv will be **TV, Tv, tV, tv**.

### Step 4: Set Up the Punnett Square
- We will set up a 4x4 Punnett square to determine the F2 generation:

| | TV | Tv | tV | tv |
|------|------|------|------|------|
| **TV** | TT VV | TT Vv | Tt VV | Tt Vv |
| **Tv** | TT Vv | TT vv | Tt Vv | Tt vv |
| **tV** | Tt VV | Tt Vv | tt VV | tt Vv |
| **tv** | Tt Vv | Tt vv | tt Vv | tt vv |

### Step 5: Count the Phenotypes in the F2 Generation
- The phenotypic ratio from the Punnett square will be:
- Tall with violet flowers (TT VV, TT Vv, Tt VV, Tt Vv): 9
- Tall with white flowers (TT vv, Tt vv): 3
- Dwarf with violet flowers (tt VV, tt Vv): 3
- Dwarf with white flowers (tt vv): 1

### Step 6: Calculate the Expected Number of Dwarf White Flower Plants
- The total ratio is 9:3:3:1, which sums to 16 parts.
- The fraction of dwarf white flower plants (tt vv) is 1 out of 16.
- If there are 176 offspring in total, we calculate the expected number of dwarf white flower plants as follows:

\[ \text{Expected number of dwarf white flower plants} = \frac{1}{16} \times 176 = 11 \]

### Final Answer
Thus, the expected number of plants that are dwarf and bearing white flowers in the F2 generation is **11**.

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