The number of recombinants in the 1280 progeny obtained through a dihybrid cross of Mendel in the F2 generation.
Show Hint
- 240
- 360
- 720
- 480
The Correct Option is D
Approach Solution - 1
Step 1: Understanding Recombinants in a Dihybrid Cross In a Mendelian dihybrid cross, the recombinant frequency follows a \(9:3:3:1\) phenotypic ratio. Recombinants are those that do not resemble the parental types.
Step 2: Calculating the Expected Recombinants The fraction of recombinants is given by: \[ \frac{3+3}{16} = \frac{6}{16} = \frac{3}{8} \] Multiplying by the total progeny: \[ \frac{3}{8} \times 1280 = 480. \]
Approach Solution -2
1. Understand Mendel's Dihybrid Cross F2 Ratio:
In a typical Mendelian dihybrid cross (e.g., RrYy x RrYy), assuming independent assortment, the F2 generation exhibits a phenotypic ratio of 9:3:3:1.
- 9/16: Dominant for both traits (Parental Type 1, e.g., Round Yellow if parents were RRYY x rryy)
- 3/16: Dominant for trait 1, Recessive for trait 2 (Recombinant Type 1, e.g., Round Green)
- 3/16: Recessive for trait 1, Dominant for trait 2 (Recombinant Type 2, e.g., Wrinkled Yellow)
- 1/16: Recessive for both traits (Parental Type 2, e.g., Wrinkled Green)
2. Identify Recombinant Phenotypes:
Recombinants are the progeny showing new combinations of traits compared to the original P generation parents. In the F2 generation, these correspond to the middle two categories of the 9:3:3:1 ratio.
3. Calculate the Proportion of Recombinants:
The proportion of recombinant phenotypes in the F2 generation is the sum of the proportions of the two recombinant classes:
Proportion of Recombinants = 3/16 (Recombinant Type 1) + 3/16 (Recombinant Type 2) = 6/16
This fraction can be simplified to 3/8.
4. Calculate the Number of Recombinants in the Given Progeny:
The total number of progeny obtained is given as 1280.
Number of Recombinants = (Proportion of Recombinants) × (Total Number of Progeny)
Number of Recombinants = (6/16) × 1280
Alternatively, using the simplified fraction:
Number of Recombinants = (3/8) × 1280
Number of Recombinants = 3 × (1280 / 8)
Number of Recombinants = 3 × 160
Number of Recombinants = 480
Conclusion: The expected number of recombinants in the 1280 progeny is 480.
This corresponds to Option D.
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