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Q3:
A diploid organism is heterozygous for 4 loci, how many types of gametes can be produced?
Solution :
Step 1: Theoretical Foundation of Gamete Formation
In a diploid organism, each locus carries two alleles. When an organism is heterozygous for a specific locus (e.g., $Aa$), it possesses two distinct alleles that segregate during Meiosis I [Per Mendel’s Law of Segregation]. For an organism heterozygous for multiple independent loci, the assortment of these alleles into gametes follows Mendel’s Law of Independent Assortment.
Step 2: Defining the Variables
Let $n$ represent the number of heterozygous loci. Given: $n = 4$. Each heterozygous locus provides $2$ alternative possibilities for the gamete (either the dominant or recessive allele).
Step 3: Deriving the Mathematical Formula
Since the segregation of alleles at one locus is independent of the segregation at other loci [Per the Principle of Independent Assortment], the total number of gametic combinations is determined by the product of the possibilities at each locus.
The formula for the number of different types of gametes produced by an organism heterozygous for $n$ loci is given by:
$N = 2^n$
Step 4: Application to the Given Problem
Substitute $n = 4$ into the derived expression:
$N = 2^4$
$N = 2 \times 2 \times 2 \times 2$
$N = 16$
Visual Representation of Independent Assortment (1 Locus Example)
Summary of Combinatorial Probability
| Number of Heterozygous Loci ($n$) | Calculation ($2^n$) | Total Types of Gametes |
|---|---|---|
| 1 | $2^1$ | 2 |
| 2 | $2^2$ | 4 |
| 3 | $2^3$ | 8 |
| 4 | $2^4$ | 16 |
Final Solution: The organism can produce $16$ different types of gametes.
More Questions from Class 12 Biology Principles of Inheritance and Variation EXERCISES
- Q1: Mention the advantages of selecting pea plant for experiment by Mendel.
- Q1: Mention the advantages of selecting pea plant for experiment by Mendel.
- Q2(a): Differentiate between the following – (a) Dominance and Recessive
- Q2(a): Differentiate between the following – (a) Dominance and Recessive
- Q2(b): Differentiate between the following – (b) Homozygous and Heterozygous
- Q2(b): Differentiate between the following – (b) Homozygous and Heterozygous
- Q2(c): Differentiate between the following – (c) Monohybrid and Dihybrid.
- Q2(c): Differentiate between the following – (c) Monohybrid and Dihybrid.
- Q3: A diploid organism is heterozygous for 4 loci, how many types of gametes can be produced?
- Q4: Explain the Law of Dominance using a monohybrid cross.
- Q4: Explain the Law of Dominance using a monohybrid cross.
- Q5: Define and design a test-cross.
- Q5: Define and design a test-cross.
- Q6: Using a Punnett Square, workout the distribution of phenotypic features in the first filial generation after a cross between a homozygous female and a heterozygous male for a single locus.
- Q6: Using a Punnett Square, workout the distribution of phenotypic features in the first filial generation after a cross between a homozygous female and a heterozygous male for a single locus.
- Q7(a): When a cross in made between tall plant with yellow seeds (\(TtYy\)) and tall plant with green seed (\(Ttyy\)), what proportions of phenotype in the offspring could be expected to be (a) tall and green.
- Q7(a): When a cross in made between tall plant with yellow seeds ((TtYy)) and tall plant with green seed ((Ttyy)), what proportions of phenotype in the offspring could be expected to be (a) tall and green.
- Q7(b): When a cross in made between tall plant with yellow seeds (\(TtYy\)) and tall plant with green seed (\(Ttyy\)), what proportions of phenotype in the offspring could be expected to be (b) dwarf and green.
- Q7(b): When a cross in made between tall plant with yellow seeds ((TtYy)) and tall plant with green seed ((Ttyy)), what proportions of phenotype in the offspring could be expected to be (b) dwarf and green.
- Q8: Two heterozygous parents are crossed. If the two loci are linked what would be the distribution of phenotypic features in \(F_{1}\) generation for a dibybrid cross?
- Q8: Two heterozygous parents are crossed. If the two loci are linked what would be the distribution of phenotypic features in (F_{1}) generation for a dibybrid cross?
- Q9: Briefly mention the contribution of T.H. Morgan in genetics.
- Q9: Briefly mention the contribution of T.H. Morgan in genetics.
- Q10: What is pedigree analysis? Suggest how such an analysis, can be useful.
- Q10: What is pedigree analysis? Suggest how such an analysis, can be useful.
- Q11: How is sex determined in human beings?
- Q11: How is sex determined in human beings?
- Q12: A child has blood group O. If the father has blood group A and mother blood group B, work out the genotypes of the parents and the possible genotypes of the other offsprings.
- Q12: A child has blood group O. If the father has blood group A and mother blood group B, work out the genotypes of the parents and the possible genotypes of the other offsprings.
- Q13(a): Explain the following terms with example (a) Co-dominance
- Q13(a): Explain the following terms with example (a) Co-dominance
- Q13(b): Explain the following terms with example (b) Incomplete dominance
- Q13(b): Explain the following terms with example (b) Incomplete dominance
- Q14: What is point mutation? Give one example.
- Q14: What is point mutation? Give one example.
- Q15: Who had proposed the chromosomal theory of the inheritance?
- Q15: Who had proposed the chromosomal theory of the inheritance?
- Q16: Mention any two autosomal genetic disorders with their symptoms.
- Q16: Mention any two autosomal genetic disorders with their symptoms.
CBSE Solutions for Class 12 Biology Principles of Inheritance and Variation
Chapters in CBSE - Class 12 Biology
- Reproduction in Organisms
- Human Reproduction
- Reproductive Health
- Molecular Basis of Inheritance
- Evolution
- Human Health and Disease
- Strategies for Enhancement in Food Production
- Microbes in Human Welfare
- Biotechnology: Principles and Processes
- Biotechnology and Its Applications
- Organisms and Populations
- Ecosystem
- Biodiversity and Conservation
- Environmental Issues
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