Board Formulas

Principles of Inheritance and Variation

Mendelian ratios, laws of inheritance, incomplete dominance, codominance, linkage, sex determination, pedigree analysis — NCERT Class 12 Biology Ch 4

📐 10 formulas✏️ 3 examples🎯 6 practice⚖️ 7-8 marks🏫 CBSE📚 Class 12✓ 2025–26 syllabus
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Board Exam Tips

  • Mendel's dihybrid cross with 9:3:3:1 ratio derivation is a 5-mark favourite — practise the Punnett square.
  • Pedigree analysis (autosomal vs sex-linked, dominant vs recessive) appears almost every year.
  • ABO blood group problem tests multiple alleles + codominance. Learn the six genotype possibilities.
  • Never confuse incomplete dominance (1:2:1) with codominance (both alleles expressed simultaneously).
  • For sex determination write XX/XY for humans, ZZ/ZW for birds, XX/XO for grasshopper. Do not mix up.

📐 Formulas(10)

1

Monohybrid Phenotypic Ratio★ Board fav

2

Monohybrid Genotypic Ratio

3

Dihybrid Phenotypic Ratio★ Board fav

4

Test Cross Ratio

5

Incomplete Dominance★ Board fav

6

ABO Blood Group Alleles

7

Sex Determination★ Board fav

8

Chromosome Numbers (Human)

9

Down Syndrome Karyotype

10

Klinefelter and Turner Karyotypes

✏️ Solved Examples

1Solved Exampleeasy4 steps

A pure-breeding tall pea plant (TT) is crossed with a pure-breeding dwarf pea plant (tt). Write the genotypes and phenotypes of the F₁ and F₂ generations.

1

Parents

2Solved Exampleboard4 steps

A man of blood group AB marries a woman of blood group O. What are the possible blood groups of their children? Show with a Punnett square. (3 marks)

1

Write parental genotypes

3Solved ExampleHOTS4 steps

A haemophilic man marries a normal woman whose father was haemophilic. Determine the probability that their (a) sons and (b) daughters will be haemophiliacs.

1

Assign genotypes (haemophilia is X-linked recessive)

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6
  • 1

    Confusing genotype (TT, Tt, tt) with phenotype (tall, dwarf)

    Genotype = allele combination; phenotype = visible trait. Tt and TT have the same phenotype but different genotypes.

  • 2

    Writing dihybrid F₂ ratio as 3:1

    Dihybrid ratio is 9:3:3:1 because two genes segregate independently. 3:1 is the monohybrid ratio.

  • 3

    Treating incomplete dominance and codominance as identical

    Incomplete dominance produces an intermediate phenotype (pink from red × white). Codominance expresses both parental phenotypes simultaneously (AB blood group).

  • 4

    Assuming mother determines sex of the child in humans

    Human females are XX (produce only X eggs). The father contributes either X (→ girl) or Y (→ boy), so the father determines sex.

  • 5

    Believing haemophilic females do not exist

    They are extremely rare but possible (XʰXʰ). Both parents must contribute an Xʰ — father must be haemophilic and mother at least a carrier.

  • 6

    Confusing linkage with independent assortment

    Genes on the same chromosome are linked and violate independent assortment; the closer they are the tighter the linkage (Morgan's work on Drosophila).

🎯 Practice Yourself

🎯Practice Yourself6 questions
  1. Q1

    State Mendel's law of segregation in one line.

  2. Q2

    In a dihybrid cross RrYy × RrYy how many phenotypes and genotypes appear in the F₂?

  3. Q3

    A test cross of a tall plant produces 50% tall and 50% dwarf offspring. What is the genotype of the tall parent?

  4. Q4

    Which blood group is called the 'universal donor' and which is the 'universal recipient'?

  5. Q5

    Why is colour-blindness more common in men than in women?

  6. Q6

    A couple with normal vision has a colour-blind son. Give the genotypes of the parents.

📝 Notes

Principles of Inheritance and Variation

NCERT Chapter 4 introduces classical genetics — from Mendel's pea experiments through chromosomal theory to modern insights on sex linkage and Mendelian disorders in humans.

Mendel's genius

Working with garden pea (Pisum sativum) between 1856 and 1863, Mendel studied seven contrasting characters, each controlled by a single gene with two alleles. His three laws:

  • Law of Dominance — in a heterozygote only the dominant allele is expressed.
  • Law of Segregation — the two alleles of a gene separate during gamete formation.
  • Law of Independent Assortment — different gene pairs segregate independently (holds only for unlinked genes).

The Punnett square

A 2×2 (monohybrid) or 4×4 (dihybrid) grid predicts F₂ ratios. Because gametes fuse randomly and each has an equal chance, the frequency of each offspring genotype is the product of the parental gamete frequencies.

Beyond Mendel — deviations

  • Incomplete dominance — heterozygote is intermediate (Mirabilis snapdragon: RR red, Rr pink, rr white). Phenotypic ratio = genotypic ratio = 1:2:1.
  • Codominance — both alleles expressed (ABO blood group: IᴬIᴮ = AB).
  • Multiple allelism — more than two alleles at a locus in the population (Iᴬ, Iᴮ, i).
  • Pleiotropy — one gene affects many characters (phenylketonuria; sickle-cell anaemia).
  • Polygenic inheritance — many genes contribute to one trait (human skin colour, height).

Linkage and recombination

Genes on the same chromosome tend to be inherited together. Morgan's Drosophila work showed:

  • Linked genes violate independent assortment.
  • Crossing-over between homologs produces recombinants.
  • Recombination frequency (units of map distance in centiMorgans) is proportional to physical distance up to about 50 cM.

Sex determination

  • XY system — humans, Drosophila. Male heterogametic (XY); female XX.
  • ZW system — birds, some reptiles. Female heterogametic (ZW); male ZZ.
  • XO system — grasshoppers. Male XO, female XX.

Because human males contribute X or Y with equal probability, sex ratio is expected to be 1:1.

Mendelian and chromosomal disorders in humans

  • Autosomal recessive — sickle-cell anaemia, phenylketonuria, cystic fibrosis, thalassemia.
  • X-linked recessive — haemophilia, colour blindness, Duchenne muscular dystrophy.
  • Autosomal dominant — Huntington's disease, myotonic dystrophy.
  • Chromosomal aneuploidies — Down syndrome (trisomy 21), Klinefelter (47, XXY), Turner (45, XO).

Pedigree analysis rules of thumb

  • Trait skips a generation → probably recessive.
  • Trait appears in every generation → probably dominant.
  • Only males affected → likely X-linked recessive.
  • Affected fathers pass to all daughters (never sons) → X-linked dominant.

Quick sanity checks

  • Monohybrid ratio: 3:1. Dihybrid: 9:3:3:1. Trihybrid: 27:9:9:9:3:3:3:1.
  • A dihybrid F₁ selfed makes 16 boxes in the Punnett square, four gamete types per parent.
  • (3:1) × (3:1) = 9:3:3:1 — the product rule in action.

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