Mendel's laws of Inheritance

Q: How is the 9 : 3 : 3 : 1 ratio obtained in a dihybrid cross?

The F1 RrYy forms four kinds of gametes, RY, Ry, rY and ry, each 1/4, because the two gene pairs segregate independently. Their 16 combinations give 9 round yellow, 3 round green, 3 wrinkled yellow and 1 wrinkled green, which is (3 : 1) multiplied by (3 : 1).

BiologyPrinciples of Inheritance and VariationFor NEET aspirants

Mendel's laws of inheritance explain how characters pass from parents to offspring in predictable ratios. This page covers genetics, inheritance and variation, Mendel's experiments on the garden pea, the monohybrid cross, the Punnett square and the test cross. It then covers the Law of Dominance, the Law of Segregation, the dihybrid cross and the Law of Independent Assortment, as in the NCERT Class 12 chapter Principles of Inheritance and Variation. NEET regularly asks the 3:1, 1:2:1 and 9:3:3:1 ratios, test-cross results and the statements of Mendel's laws of inheritance.

On this page1Genetics2Mendel's experiments3Monohybrid cross4Genes and alleles5Punnett square6Test cross7Dominance and segregation8Dihybrid cross9Independent assortment10Exam essentials11Quick revision12Solved examples13Practice

Key Points at a Glance

★ Must learn Genetics deals with the inheritance and variation of characters from parents to offspring.
Mendel worked on the garden pea for 7 years (1856-1863), with 14 true-breeding varieties and 7 pairs of contrasting traits.
★ Must learn Monohybrid cross TT × tt: all F₁ tall; F₂ phenotypic ratio 3 : 1 and genotypic ratio 1 : 2 : 1.
Genes (Mendel's factors) are the units of inheritance; alleles are slightly different forms of the same gene.
★ Must learn Test cross: dominant phenotype × recessive parent. Progeny 1 : 1 means heterozygous; all dominant means homozygous.
Law of Dominance: factors occur in pairs, and in a dissimilar pair one factor dominates the other.
★ Must learn Law of Segregation: the two alleles separate at gamete formation, so each gamete gets only one allele.
★ Must learn Dihybrid cross RRYY × rryy: F₂ ratio 9 : 3 : 3 : 1, from 16 combinations, 9 genotypes and 4 phenotypes.
Law of Independent Assortment: in a dihybrid, one pair of characters segregates independently of the other pair.
Monohybrid F₂ as a binomial: $(\frac{1}{2} T + \frac{1}{2} t)^{2} = \frac{1}{4} T T + \frac{1}{2} T t + \frac{1}{4} tt$ .

1. Genetics, Inheritance and Variation

An elephant gives birth only to a baby elephant, and a mango seed forms only a mango plant. Yet offspring are not identical to their parents.
Genetics: the branch of biology that deals with the inheritance, as well as the variation, of characters from parents to offspring.
★ Exam imp Inheritance: the process by which characters are passed on from parent to progeny. It is the basis of heredity.
Variation: the degree by which progeny differ from their parents.
Progeny resemble their parents in morphological and physiological features; this resemblance has long attracted biologists.
As early as 8000-1000 B.C., humans knew that one cause of variation was hidden in sexual reproduction.
They used the variation present in wild plants and animals to selectively breed organisms with desirable characters.
Example: artificial selection and domestication of ancestral wild cows gave well-known Indian breeds, such as Sahiwal cows in Punjab.
Our ancestors knew about inheritance and variation, but they had very little idea of the scientific basis of these phenomena.

Inheritance

Characters pass from parent to progeny
Basis of heredity
Explains why offspring resemble parents

Variation

Degree to which progeny differ from parents
One cause hidden in sexual reproduction
Used by humans for selective breeding

Key idea

Inheritance makes offspring resemble their parents; variation makes them differ. Genetics studies both.

2. Mendel's Experiments on the Garden Pea

Real progress in understanding inheritance came only in the mid-nineteenth century.
Mendel was the first to study inheritance systematically.
★ Exam imp Gregor Mendel conducted hybridisation experiments on garden peas for seven years (1856-1863) and proposed the laws of inheritance in living organisms.
For the first time, statistical analysis and mathematical logic were applied to problems in biology.
His experiments had a large sampling size, which gave greater credibility to his data.
He confirmed his inferences on successive generations of test plants. So his results pointed to general rules of inheritance, not unsupported ideas.
He studied characters that showed two opposing traits, for example tall or dwarf plants, and yellow or green seeds.
This gave a basic framework of rules. Later scientists expanded it to explain the diverse, complex observations in nature.
He carried out artificial pollination (cross pollination) experiments using several true-breeding pea lines.

★ Very important True-breeding line: a line that, after continuous self-pollination, shows stable inheritance and expression of a trait for several generations. Mendel selected 14 true-breeding pea varieties as pairs that were similar except for one character with contrasting traits.

Contrasting traits he selected included smooth or wrinkled seeds, yellow or green seeds, inflated (full) or constricted pods, green or yellow pods, and tall or dwarf plants.

Seven pairs of contrasting traits in pea studied by Mendel

S. No.	Character	Dominant trait	Recessive trait
1	Stem height	Tall	Dwarf
2	Flower colour	Violet	White
3	Flower position	Axial	Terminal
4	Pod shape	Inflated (full)	Constricted
5	Pod colour	Green	Yellow
6	Seed shape	Round	Wrinkled
7	Seed colour	Yellow	Green

Test yourself: hide labels

Figure 1: Seven pairs of contrasting traits in the pea plant studied by Mendel. For each character, the dominant trait is in the middle column and the recessive trait in the right column.

Memory Trick Group the 7 characters by organ: 2 seed + 2 pod + 2 flower + 1 stem = 7. Dominant traits in the same order: round, yellow (seed); inflated, green (pod); violet, axial (flower); tall (stem). Seed yellow, pod green: the dominant colours swap between the seed and the pod.

NEET Focus Students often swap the colours. Green is dominant for pod colour, but yellow is dominant for seed colour. Axial (not terminal) flower position is dominant, and inflated (not constricted) pod shape is dominant.

Key idea

Mendel's success came from true-breeding lines, single contrasting traits, large samples and statistics.

3. Inheritance of One Gene: The Monohybrid Cross

Mendel crossed tall and dwarf pea plants to study the inheritance of one gene.

3.1 Steps in making a cross

Choose two true-breeding parents with contrasting traits; one acts as the female (♀) parent, the other as the male (♂) parent.
Remove the anthers from the flower of the female parent. This is emasculation.
Transfer pollen from the male parent to the stigma of the emasculated flower. This is pollination.
Collect the seeds formed in the pod, and grow them into plants of the first hybrid generation.

Test yourself: hide labels

Figure 2: Steps in making a cross in pea. The anthers of the female parent are removed (emasculation), pollen from the male parent is placed on its stigma (pollination), and the seeds grow into the next generation.

3.2 The F₁ and F₂ generations

The plants of the first hybrid generation are called the Filial₁ progeny, or the F₁.
★ Exam imp All F₁ plants were tall, like one of the parents; none were dwarf.
The same happened for the other pairs of traits: the F₁ always resembled one parent, and the trait of the other parent was not seen.
Mendel then self-pollinated the tall F₁ plants to obtain the Filial₂ (F₂) generation.
Some F₂ offspring were dwarf: the character not seen in the F₁ was expressed again.
★ Exam imp 1/4 of the F₂ plants were dwarf and 3/4 were tall.
The tall and dwarf F₂ plants were identical to their parental types. There was no blending: no plant was of in-between height.
Similar results came with every trait: only one parental trait in the F₁, and both traits in the F₂ in the proportion 3 : 1.
The contrasting traits did not blend at either the F₁ or the F₂ stage.

Test yourself: hide labels

Figure 3: Diagrammatic representation of a monohybrid cross. All F₁ plants are tall; selfing them gives tall and dwarf F₂ plants in the ratio 3 : 1.

Memory Trick F₁ hides, F₂ reveals. The recessive trait is hidden in the F₁ and comes back unchanged in one-fourth of the F₂.

Key idea

No blending: the F₁ looks like one parent, and the F₂ shows both parental traits in a 3 : 1 ratio.

4. Factors, Genes and Alleles

Mendel proposed that something is passed down stably and unchanged from parent to offspring through the gametes, over successive generations.
He called these things factors. Today they are called genes.
★ Exam imp Genes are the units of inheritance. They contain the information required to express a particular trait in an organism.
Alleles: genes that code for a pair of contrasting traits. They are slightly different forms of the same gene.
Symbols: a capital letter stands for the trait expressed at the F₁ stage, and the small letter for the other trait.
For height, T stands for tall and t for dwarf; T and t are alleles of each other.
So the pair of alleles for height in a pea plant can be TT, Tt or tt.
Do not use T for tall and d for dwarf. It then becomes hard to remember whether T and d are alleles of the same gene.
In a true-breeding tall or dwarf variety, the two alleles for height are identical: homozygous, TT or tt.
TT and tt are the genotypes of the plants; the descriptive terms tall and dwarf are their phenotypes.

4.1 Dominant and recessive

Mendel found that the F₁ heterozygote Tt looks exactly like the TT parent.
So in a pair of dissimilar factors, one dominates the other: it is the dominant factor, and the other is recessive.
Here T (tallness) is dominant over t (dwarfness), which is recessive.
He observed identical behaviour for all the other pairs of traits he studied.
Alleles can be similar, as in the homozygotes TT and tt, or dissimilar, as in the heterozygote Tt.
Tt is heterozygous for genes controlling one character (height). So it is a monohybrid, and TT × tt is a monohybrid cross.

Term	Meaning	Example
Gene (factor)	Unit of inheritance; carries information for a trait	Gene for height
Allele	Slightly different form of the same gene	T and t
Homozygous	Both alleles of the pair identical	TT, tt
Heterozygous	The two alleles of the pair dissimilar	Tt
Genotype	Allelic make-up of an organism	TT, Tt, tt
Phenotype	Observable (descriptive) trait	Tall, dwarf
Dominant	Allele expressed in the heterozygote	T
Recessive	Allele not expressed in the heterozygote	t
Monohybrid	Heterozygous for genes of one character	Tt

Homozygous

Identical alleles: TT or tt
True-breeding
Forms one kind of gamete

Heterozygous

Dissimilar alleles: Tt
Hybrid; does not breed true
Forms two kinds of gametes in equal proportion

★ Very important Genotype is the allelic make-up (TT, Tt, tt); phenotype is the trait we see (tall, dwarf). TT and Tt have the same phenotype but different genotypes.

Quick Recall: tap to check

What did Mendel call the units we now call genes?

Factors.

Why should tall and dwarf be written as T and t, not T and d?

Capital and small forms of one letter show at once that they are alleles of the same gene; T and d would hide this.

Is Tt a monohybrid?

Yes. It is heterozygous for genes controlling one character, height.

Key idea

A gene comes in alleles; the dominant allele decides the phenotype of the heterozygote.

5. Segregation of Alleles and the Punnett Square

The recessive parental trait reappears in the F₂ without any blending.
★ Exam imp So when the tall and dwarf plants form gametes by meiosis, the alleles of the parental pair separate (segregate), and only one allele passes to a gamete.
This segregation is random: a gamete has a 50 per cent chance of carrying either allele, as the crosses confirm.
Gametes of the tall TT plants carry T; gametes of the dwarf tt plants carry t.
At fertilisation, T from one parent (say, through the pollen) unites with t from the other (through the egg).
The zygotes, and so the hybrids, are Tt. Since they carry alleles for contrasting traits, they are heterozygous.

★ Very important Punnett square: a graphical representation used to calculate the probability of all possible genotypes of offspring in a genetic cross. It was developed by the British geneticist Reginald C. Punnett. The possible gametes are written on two sides, usually the top row and the left column, and all combinations fill the boxes below.

The tall TT (male) and dwarf tt (female) parents form gametes T and t; fertilisation gives F₁ progeny Tt.
The F₁ plants of genotype Tt are self-pollinated. The symbol ♀ denotes the female (eggs) and ♂ the male (pollen) of the F₁.
Each F₁ plant forms gametes T and t in equal proportion.
A pollen grain T has a 50 per cent chance of pollinating an egg T and a 50 per cent chance of pollinating an egg t.
A pollen grain t likewise has a 50 per cent chance of pollinating an egg T or an egg t.
Random fertilisation therefore gives zygotes of genotype TT, Tt or tt.

Test yourself: hide labels

Figure 4: A Punnett square for Mendel's monohybrid cross between true-breeding tall and dwarf plants. The F₂ has 3 tall : 1 dwarf, but genotypes 1 TT : 2 Tt : 1 tt.

★ Exam imp From the Punnett square, 1/4 of the random fertilisations give TT, 1/2 give Tt and 1/4 give tt.
The F₁ has genotype Tt, but its phenotype is tall.
In the F₂, 3/4 of the plants are tall: some are TT and others Tt. Externally, TT and Tt plants cannot be told apart.
In the genotypic pair Tt, only the character T (tall) is expressed. So T is said to dominate over the allele t (dwarf).
Because of this dominance, all the F₁ are tall, and 3/4 of the F₂ are tall although only 1/4 are TT and 1/2 are Tt.
This gives a phenotypic ratio of 3 : 1 (3/4 tall, made of 1/4 TT + 1/2 Tt, and 1/4 tt dwarf) but a genotypic ratio of 1 : 2 : 1.

The ratio 1/4 : 1/2 : 1/4 of TT : Tt : tt is the expansion of the binomial $(a x + b y)^{2}$ , since gametes carry T or t with equal frequency, 1/2:

(\frac{1}{2} T + \frac{1}{2} t)^{2} = (\frac{1}{2} T + \frac{1}{2} t) \times (\frac{1}{2} T + \frac{1}{2} t) = \frac{1}{4} T T + \frac{1}{2} T t + \frac{1}{4} tt

Mendel self-pollinated the F₂ plants. The dwarf F₂ plants gave only dwarf plants in the F₃ and F₄ generations.
So he concluded that the genotype of the dwarfs was homozygous, tt.
A tall F₂ plant, when self-pollinated, behaves in one of two ways: a TT plant gives only tall plants, while a Tt plant gives tall and dwarf plants in a 3 : 1 ratio.

Memory Trick The 1 : 2 : 1 hides inside the 3 : 1. The ‘3’ of the phenotypic ratio is 1 TT + 2 Tt; the ‘1’ is tt. Add the first two numbers of 1 : 2 : 1 to get 3 : 1.

Key idea

Segregation plus random fertilisation gives 1 TT : 2 Tt : 1 tt, which dominance turns into 3 tall : 1 dwarf.

6. The Test Cross

Genotypic ratios can be calculated by probability, but the phenotype of a dominant trait does not reveal its genotype.
For example, whether a tall F₁ or F₂ plant is TT or Tt cannot be predicted by looking at it.
To find the genotype of a tall F₂ plant, Mendel crossed it with a dwarf plant. He called this a test cross.

★ Very important Test cross: a cross in which an organism showing the dominant phenotype, whose genotype is to be determined, is crossed with the recessive parent instead of being self-crossed. The progeny are easily analysed to predict the genotype of the test organism.

In the example below, violet flower colour (W) is dominant over white flower colour (w).

Test yourself: hide labels

Figure 5: Diagrammatic representation of a test cross. All violet progeny show that the unknown plant is WW; half violet and half white (1 : 1) show that it is Ww.

Unknown plant	Cross	Progeny	Ratio	Conclusion
WW	WW × ww	All Ww, violet	All dominant	Homozygous dominant
Ww	Ww × ww	Ww violet and ww white	1 : 1	Heterozygous

Tips and Tricks Test-cross ratios are the quickest give-away in a question. A 1 : 1 progeny ratio means the tested parent was heterozygous; all-dominant progeny mean it was homozygous. In general terms, a test cross is the cross of an organism of dominant phenotype with its homozygous recessive parent.

Extra Depth: A test cross of a dihybrid heterozygote (RrYy × rryy) gives four phenotypes in the ratio 1 : 1 : 1 : 1 when the two genes assort independently.

Key idea

A test cross uses the homozygous recessive parent to expose the hidden genotype of a dominant-looking organism.

7. The Laws of Dominance and Segregation

From his monohybrid crosses, Mendel proposed two general rules. Today they are called the Principles or Laws of Inheritance.
★ Exam imp The First Law is the Law of Dominance, and the Second Law is the Law of Segregation.

7.1 Law of Dominance

Characters are controlled by discrete units called factors.
Factors occur in pairs.
In a dissimilar pair of factors, one member of the pair dominates (dominant) the other (recessive).

The law explains why only one parental character is expressed in the F₁ of a monohybrid cross, and both are expressed in the F₂.
It also explains the 3 : 1 proportion obtained at the F₂.

7.2 Law of Segregation

It rests on two facts: the alleles do not blend, and both characters are recovered as such in the F₂, though one is not seen at the F₁ stage.
★ Exam imp Parents contain two alleles, but during gamete formation the factors (alleles) of a pair segregate, so that a gamete receives only one of the two factors.
A homozygous parent produces gametes that are all similar.
A heterozygous parent produces two kinds of gametes, each with one allele, in equal proportion.

Law of Dominance (First Law)

Factors occur in pairs
One factor of a dissimilar pair dominates
Explains the F₁ and the 3 : 1

Law of Segregation (Second Law)

Alleles do not blend
Alleles of a pair separate at gamete formation
Each gamete gets only one allele

Memory Trick D-S from one gene, I from two genes. The monohybrid cross gave the Law of Dominance (first) and the Law of Segregation (second); the dihybrid cross gave the Law of Independent Assortment.

Key idea

Dominance explains what the F₁ shows; segregation explains why the recessive trait returns unchanged in the F₂.

8. Inheritance of Two Genes: The Dihybrid Cross

Mendel also crossed pea plants that differed in two characters.
Example: a plant with yellow, round seeds crossed with a plant with green, wrinkled seeds.
All the seeds from this cross were yellow and round. So yellow is dominant over green, and round is dominant over wrinkled.
These results matched his separate monohybrid crosses between yellow and green, and between round and wrinkled seeded plants.
Symbols: Y for dominant yellow and y for recessive green seed colour; R for round and r for wrinkled seed shape.

Parents: RRYY (round, yellow) × rryy (wrinkled, green).
Gametes: RY from one parent and ry from the other.
Fertilisation gives the F₁ hybrid RrYy (round, yellow).
The F₁ is self-hybridised (selfed).
In the F₂, 3/4 of the plants have yellow seeds and 1/4 green: colour segregates 3 : 1.
Round and wrinkled seed shape also segregate 3 : 1, just as in a monohybrid cross.

Test yourself: hide labels

Figure 6: Results of a dihybrid cross between parents differing in seed colour and seed shape. The 16 F₂ combinations give round yellow : round green : wrinkled yellow : wrinkled green = 9 : 3 : 3 : 1.

Key idea

In a dihybrid cross, each character still segregates 3 : 1, exactly as in a monohybrid cross.

9. The Law of Independent Assortment

★ Exam imp In the dihybrid F₂, the phenotypes round yellow, wrinkled yellow, round green and wrinkled green appeared in the ratio 9 : 3 : 3 : 1.
Mendel observed this ratio for several pairs of characters.
The 9 : 3 : 3 : 1 ratio is a combination of the series 3 yellow : 1 green with 3 round : 1 wrinkled:

(3 Round : 1 Wrinkled) (3 Yellow : 1 Green) = 9 Round, Yellow : 3 Wrinkled, Yellow : 3 Round, Green : 1 Wrinkled, Green

Dihybrid cross: a cross between plants that differ in two traits.
From such crosses Mendel proposed a second set of generalisations, the Law of Independent Assortment.

★ Very important Law of Independent Assortment: when two pairs of traits are combined in a hybrid, the segregation of one pair of characters is independent of the other pair of characters.

9.1 Gametes of the F₁ dihybrid

The Punnett square shows the independent segregation of the two gene pairs during meiosis, as the F₁ RrYy plant produces eggs and pollen.
Consider R and r: 50 per cent of the gametes have R, and the other 50 per cent have r.
Besides R or r, each gamete must also carry Y or y.
★ Exam imp The segregation of 50 per cent R and 50 per cent r is independent of the segregation of 50 per cent Y and 50 per cent y.
So 50 per cent of the r-bearing gametes have Y and 50 per cent have y; the same is true of the R-bearing gametes.
Thus there are four kinds of gametes (four kinds of pollen and four kinds of eggs): RY, Ry, rY and ry, each with a frequency of 25 per cent (1/4).
Writing these on the two sides of a Punnett square gives 16 squares, from which the zygotes forming the F₂ plants are easily derived.

Genotypes found in the F₂ of the dihybrid cross

S. No.	Genotype in F₂	Number out of 16	Expected phenotype
1	RRYY	1	Round, yellow
2	RRYy	2	Round, yellow
3	RrYY	2	Round, yellow
4	RrYy	4	Round, yellow
5	RRyy	1	Round, green
6	Rryy	2	Round, green
7	rrYY	1	Wrinkled, yellow
8	rrYy	2	Wrinkled, yellow
9	rryy	1	Wrinkled, green

So the 16 squares give 9 genotypes but only 4 phenotypes.
The genotypic ratio is 1 : 2 : 2 : 4 : 1 : 2 : 1 : 2 : 1. It is not 9 : 3 : 3 : 1, which is the phenotypic ratio.

Memory Trick 1-2-2-4 builds the 9: RRYY (1) + RRYy (2) + RrYY (2) + RrYy (4) = 9 round yellow. The double heterozygote RrYy is the single most frequent genotype, 4 of 16.

Tips and Tricks Count gamete types as 2ⁿ, where n is the number of heterozygous gene pairs that assort independently: Tt gives 2, RrYy gives 4, and a plant heterozygous at 4 loci gives 16. For a probability, multiply the separate monohybrid probabilities: in TtYy × Ttyy, tall and green = 3/4 × 1/2 = 3/8.

Quick Recall: tap to check

How many kinds of gametes does an RrYy plant form, and in what proportion?

Four: RY, Ry, rY and ry, each 1/4 (25 per cent).

How many genotypes and phenotypes appear in the dihybrid F2?

9 genotypes and 4 phenotypes, from 16 combinations.

Which F2 phenotype is the rarest, and what is its genotype?

Wrinkled green, rryy: 1 in 16.

Key idea

Two gene pairs that segregate independently give four gamete types in equal proportion, and hence 9 : 3 : 3 : 1.

10. Exam Essentials

Pairs to Match

Term or person	Matches with
Gregor Mendel	Hybridisation experiments on pea, 1856-1863
Reginald C. Punnett	Punnett square (British geneticist)
Sahiwal cow	Indian breed from artificial selection (Punjab)
True-breeding line	Stable trait over several generations of self-pollination
Emasculation	Removal of anthers from the female parent
Test cross	Dominant phenotype × recessive parent
Monohybrid F₂ phenotypic ratio	3 : 1
Monohybrid F₂ genotypic ratio	1 : 2 : 1
Monohybrid test cross (heterozygote)	1 : 1
Dihybrid F₂ phenotypic ratio	9 : 3 : 3 : 1
First Law	Law of Dominance
Second Law	Law of Segregation
Dihybrid cross	Law of Independent Assortment
Pod colour (dominant)	Green
Seed colour (dominant)	Yellow

Exceptions

Pod colour: green is dominant, unlike seed colour, where yellow is dominant.
Flower position: axial is dominant; terminal is recessive.
Only the homozygous recessive (tt) shows the recessive trait; Tt does not.
A test cross uses the recessive parent, not self-pollination.
9 : 3 : 3 : 1 is a phenotypic ratio; the dihybrid genotypic ratio is not 9 : 3 : 3 : 1.
In Mendel's pea crosses, the F₁ never showed an in-between trait: there was no blending.

Numbers to Remember

8000-1000 B.C.: humans already linked variation with sexual reproduction.
7 years (1856-1863): Mendel's hybridisation experiments.
14 true-breeding varieties; 7 pairs of contrasting traits.
50 per cent: chance that a gamete carries either allele.
Monohybrid F₂: 3 : 1 (phenotype), 1 : 2 : 1 (genotype); 1/4 TT, 1/2 Tt, 1/4 tt.
Dihybrid: 4 gamete types of 25 per cent each; 16 combinations; 9 genotypes; 4 phenotypes; 9 : 3 : 3 : 1.

Tips and Tricks Read the ratio, name the cross. 3 : 1 means a monohybrid F₂; 1 : 2 : 1 is its genotype ratio; 1 : 1 means a monohybrid test cross of a heterozygote; 9 : 3 : 3 : 1 means a dihybrid F₂ with independent assortment.

11. Quick Revision

Genetics: inheritance and variation; inheritance is the basis of heredity.
Sahiwal cows: an Indian breed obtained by artificial selection from wild cows.
Mendel: garden pea, 1856-1863, statistics, large samples, true-breeding lines.
14 true-breeding varieties; 7 contrasting trait pairs; pod green and seed yellow are dominant.
Cross: emasculation, then pollination, then seeds grown to get the F₁.
Tall × dwarf: F₁ all tall; F₂ 3 tall : 1 dwarf; no blending.
Factors = genes, the units of inheritance; alleles = slightly different forms of a gene.
Homozygous TT/tt; heterozygous Tt; genotype vs phenotype.
Alleles segregate at meiosis; each gamete has one allele, with a 50 per cent chance.
Punnett square (R.C. Punnett): F₂ 1 TT : 2 Tt : 1 tt; binomial (1/2 T + 1/2 t)².
Dwarf F₂ plants bred true to F₃ and F₄: they are tt.
Test cross: dominant phenotype × recessive parent; 1 : 1 = heterozygous.
Law of Dominance (3 points) and Law of Segregation (one allele per gamete).
Dihybrid RRYY × rryy: F₁ RrYy; four gametes; F₂ 9 : 3 : 3 : 1.
Law of Independent Assortment: one pair of characters segregates independently of the other.

12. Solved Examples

Solved Example 1

Match List I with List II.
List I: A. Law of Dominance, B. Law of Segregation, C. Law of Independent Assortment, D. Test cross
List II: I. Derived from dihybrid crosses, II. Factors occur in pairs and one member of a dissimilar pair dominates, III. Crossing a dominant phenotype with the recessive parent, IV. A gamete receives only one of the two factors
Choose the correct answer:
(A) A-II, B-IV, C-I, D-III
(B) A-IV, B-II, C-I, D-III
(C) A-II, B-I, C-IV, D-III
(D) A-III, B-IV, C-I, D-II

Solution:

Answer: (A). The Law of Dominance says factors occur in pairs and one dominates (II). The Law of Segregation says each gamete gets one factor (IV). Independent assortment came from dihybrid crosses (I). A test cross uses the recessive parent (III).

Solved Example 2

Read the statements about Mendel's experiments.
A. Mendel worked on the garden pea for seven years, from 1856 to 1863.
B. He selected 14 true-breeding pea varieties.
C. In pea, yellow pod colour is dominant over green pod colour.
D. He was the first to apply statistical analysis and mathematical logic to problems in biology.
E. The F₁ of a cross between tall and dwarf plants was of intermediate height.
Choose the correct answer:
(A) A, B and D only
(B) A, C and D only
(C) B, C and E only
(D) A, B, D and E only

Solution:

Answer: (A). C is wrong: green pod colour is dominant. E is wrong: all F₁ plants were tall, with no blending. A, B and D are correct.

Solved Example 3

Arrange the steps of making a cross in pea in the correct order.
A. Transfer pollen from the male parent to the stigma
B. Remove the anthers of the female-parent flower
C. Grow the seeds to get the F₁ plants
D. Select true-breeding parents with contrasting traits
E. Collect the seeds formed in the pod
Choose the correct answer:
(A) D, A, B, E, C
(B) D, B, A, E, C
(C) B, D, A, E, C
(D) D, B, A, C, E

Solution:

Answer: (B). Select parents (D), emasculate (B), pollinate (A), collect seeds (E), then grow the F₁ (C).

Solved Example 4

A violet-flowered pea plant is test-crossed with a white-flowered plant. Of the progeny, 52 are violet and 48 are white. What is the genotype of the violet parent?
(A) WW
(B) Ww
(C) ww
(D) Cannot be predicted

Solution:

Answer: (B). The progeny are close to 1 : 1. A 1 : 1 ratio in a test cross shows that the tested parent was heterozygous, Ww; a WW parent would give only violet progeny.

Solved Example 5

Which of the following is NOT correct about the F₂ of Mendel's dihybrid cross between RRYY and rryy?
(A) There are 16 combinations of gametes
(B) There are 9 different genotypes
(C) The genotypic ratio is 9 : 3 : 3 : 1
(D) 1/16 of the plants are wrinkled and green

Solution:

Answer: (C). 9 : 3 : 3 : 1 is the phenotypic ratio. The genotypic ratio is 1 : 2 : 2 : 4 : 1 : 2 : 1 : 2 : 1, from 9 genotypes.

Solved Example 6

Statement I: In a monohybrid cross, the F₂ genotypic ratio is 1 : 2 : 1.
Statement II: Tall TT and tall Tt plants cannot be distinguished by their phenotype.
(A) Both Statement I and Statement II are correct
(B) Statement I is correct but Statement II is incorrect
(C) Statement I is incorrect but Statement II is correct
(D) Both Statement I and Statement II are incorrect

Solution:

Answer: (A). The F₂ has 1/4 TT, 1/2 Tt and 1/4 tt. Because T is dominant, TT and Tt plants both look tall; only a test cross or selfing tells them apart.

13. Practice Questions

Practice Questions

Match List I (character) with List II (dominant trait in pea).
List I: A. Pod colour, B. Seed colour, C. Flower position, D. Pod shape
List II: I. Axial, II. Yellow, III. Inflated, IV. Green
(A) A-IV, B-II, C-I, D-III (B) A-II, B-IV, C-I, D-III (C) A-IV, B-II, C-III, D-I (D) A-II, B-IV, C-III, D-IAnswer: (A). Green pod, yellow seed, axial flowers and inflated pods are dominant.
Read the statements.
A. Alleles are slightly different forms of the same gene.
B. A heterozygous parent produces two kinds of gametes in equal proportion.
C. A homozygous parent produces two kinds of gametes.
D. Segregation of alleles takes place during meiosis.
Choose the correct answer: (A) A, B and D only (B) A and C only (C) B, C and D only (D) A, B, C and DAnswer: (A). C is wrong: a homozygous parent produces only one kind of gamete.
Arrange the events in order for a monohybrid cross: A. Self-pollination of the F₁, B. Formation of F₂ in a 3 : 1 ratio, C. Cross between true-breeding tall and dwarf plants, D. All F₁ plants tall.
(A) C, D, A, B (B) C, A, D, B (C) D, C, A, B (D) C, D, B, AAnswer: (A). Parental cross, all-tall F₁, selfing, then the 3 : 1 F₂.
Which of the following is NOT a feature of the Law of Dominance? (A) Characters are controlled by discrete units called factors (B) Factors occur in pairs (C) The two factors blend in the heterozygote (D) One member of a dissimilar pair dominates the otherAnswer: (C). Factors do not blend; the other three are the three points of the law.
In the F₂ of the dihybrid cross RRYY × rryy, what fraction of the plants is homozygous for both genes? (A) 1/16 (B) 1/4 (C) 9/16 (D) 1/2Answer: (B). RRYY, RRyy, rrYY and rryy are 1/16 each, so 4/16 = 1/4.
Statement I: Mendel's Law of Independent Assortment was based on dihybrid crosses.
Statement II: In a dihybrid cross, each character separately segregates in a 3 : 1 ratio.
(A) Both correct (B) I correct, II incorrect (C) I incorrect, II correct (D) Both incorrectAnswer: (A). Both are correct; the 9 : 3 : 3 : 1 is the product of two 3 : 1 ratios.
Mention the advantages of selecting the pea plant for experiments by Mendel.Answer: Pea has many clear contrasting traits (7 pairs used), true-breeding lines are available because it self-pollinates, artificial cross pollination is easy, and it gives large numbers of progeny for statistical analysis over successive generations.
Differentiate between: (a) dominance and recessive, (b) homozygous and heterozygous, (c) monohybrid and dihybrid.Answer: (a) A dominant allele is expressed in the heterozygote; a recessive allele is expressed only when homozygous. (b) Homozygous: identical alleles (TT, tt); heterozygous: dissimilar alleles (Tt). (c) Monohybrid: heterozygous for one character (Tt); dihybrid: heterozygous for two characters (RrYy).
A diploid organism is heterozygous for 4 loci. How many types of gametes can be produced?Answer: 2⁴ = 16 types, assuming the four loci assort independently.
Explain the Law of Dominance using a monohybrid cross.Answer: Cross TT (tall) × tt (dwarf): the F₁ Tt are all tall, so T dominates t. Selfing the F₁ gives 3 tall : 1 dwarf in the F₂, since TT and Tt are both tall. Factors occur in pairs, and in a dissimilar pair one dominates.
Define and design a test cross.Answer: A cross of an organism with the dominant phenotype and unknown genotype with the homozygous recessive. Example: violet (W_) × white (ww). All violet progeny means WW; violet and white in 1 : 1 means Ww.
Using a Punnett square, work out 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.Answer: If the female is AA: AA × Aa gives 1 AA : 1 Aa, all with the dominant phenotype. If the female is aa: aa × Aa gives 1 Aa : 1 aa, so 1 dominant : 1 recessive.
When a cross is made between a tall plant with yellow seeds (TtYy) and a tall plant with green seeds (Ttyy), what proportion of the offspring will be (a) tall and green, (b) dwarf and green?Answer: (a) 3/8. (b) 1/8. Height gives 3/4 tall and 1/4 dwarf; colour gives 1/2 green.

Common Mistakes to Avoid

Watch out

Writing yellow as the dominant pod colour. Correct: green pods and yellow seeds are dominant.
Using T and d for tall and dwarf. Correct: use one letter, T and t, for the two alleles of one gene.
Calling 9 : 3 : 3 : 1 a genotypic ratio. Correct: it is the phenotypic ratio; the dihybrid F₂ has 9 genotypes.
Saying the F₁ of tall × dwarf is of medium height. Correct: all F₁ plants are tall; there is no blending.
Crossing the unknown with the dominant parent in a test cross. Correct: a test cross uses the recessive parent.
Saying a heterozygote forms one kind of gamete. Correct: it forms two kinds, in equal proportion.
Calling the Law of Independent Assortment the second law. Correct: dominance is the first law and segregation the second; independent assortment comes from dihybrid crosses.
Reading 1 : 1 in a test cross as homozygous. Correct: 1 : 1 means the tested parent is heterozygous.

Frequently Asked Questions

What are Mendel's laws of inheritance?

Mendel's monohybrid crosses gave the Law of Dominance (first law) and the Law of Segregation (second law). His dihybrid crosses gave the Law of Independent Assortment. Together they explain how factors (genes) pass from parents to offspring and why the 3 : 1 and 9 : 3 : 3 : 1 ratios appear.

Why did Mendel choose the garden pea?

The pea shows many pairs of clear contrasting traits, and true-breeding lines are available because it self-pollinates. Artificial cross pollination is easy, and each cross gives many seeds. This allowed large samples and statistical analysis over successive generations.

What is the difference between genotype and phenotype?

The genotype is the allelic make-up of an organism, such as TT, Tt or tt for height. The phenotype is the observable trait, such as tall or dwarf. TT and Tt plants have different genotypes but the same tall phenotype, because T is dominant.

Why is the monohybrid F2 phenotypic ratio 3 : 1 but the genotypic ratio 1 : 2 : 1?

Random fertilisation gives 1/4 TT, 1/2 Tt and 1/4 tt, so the genotypic ratio is 1 : 2 : 1. Because T is dominant, both TT and Tt plants are tall. So 3/4 of the plants are tall and 1/4 dwarf, a phenotypic ratio of 3 : 1.

What is a test cross and why is it used?

A test cross crosses an organism showing the dominant phenotype with the homozygous recessive parent. It reveals the unknown genotype. If all the progeny show the dominant trait, the parent is homozygous; if dominant and recessive progeny appear in a 1 : 1 ratio, it is heterozygous.

What does the Law of Segregation state?

Alleles do not blend. During gamete formation, the two factors (alleles) of a pair separate, so that each gamete receives only one of them. A homozygous parent forms one kind of gamete, while a heterozygous parent forms two kinds in equal proportion.

How is the 9 : 3 : 3 : 1 ratio obtained in a dihybrid cross?

The F₁ RrYy forms four kinds of gametes, RY, Ry, rY and ry, each 1/4, because the two gene pairs segregate independently. Their 16 combinations give 9 round yellow, 3 round green, 3 wrinkled yellow and 1 wrinkled green, which is (3 : 1) multiplied by (3 : 1).

How many types of gametes does an organism heterozygous for several genes form?

If the genes assort independently, the number of gamete types is 2 raised to the number of heterozygous gene pairs. Tt forms 2 types, RrYy forms 4 types, and an organism heterozygous at 4 loci forms 16 types.

Previous year questions on Mendel's laws of Inheritance

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1. Genetics, Inheritance and Variation

2. Mendel's Experiments on the Garden Pea

3. Inheritance of One Gene: The Monohybrid Cross

3.1 Steps in making a cross

3.2 The F1 and F2 generations

4. Factors, Genes and Alleles

4.1 Dominant and recessive

5. Segregation of Alleles and the Punnett Square

6. The Test Cross

7. The Laws of Dominance and Segregation

7.1 Law of Dominance

7.2 Law of Segregation

8. Inheritance of Two Genes: The Dihybrid Cross

9. The Law of Independent Assortment

9.1 Gametes of the F1 dihybrid

10. Exam Essentials

11. Quick Revision

12. Solved Examples

13. Practice Questions

Common Mistakes to Avoid

Frequently Asked Questions

What are Mendel's laws of inheritance?

Why did Mendel choose the garden pea?

What is the difference between genotype and phenotype?

Why is the monohybrid F2 phenotypic ratio 3 : 1 but the genotypic ratio 1 : 2 : 1?

What is a test cross and why is it used?

What does the Law of Segregation state?

How is the 9 : 3 : 3 : 1 ratio obtained in a dihybrid cross?

How many types of gametes does an organism heterozygous for several genes form?

Previous year questions on Mendel's laws of Inheritance

Ready to master Principles of Inheritance and Variation?

3.2 The F₁ and F₂ generations

9.1 Gametes of the F₁ dihybrid