Q.A student performed some crosses in plants and represented the result in the form of bar graphs as shown below. Each graph displays the phenotypic proportion of the progeny. Study the graphs and answer the questions :
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Start your 14-day free trial to unlock the full solution →Concept understanding — Dihybrid Cross Ratio
Let’s begin with something you already know from everyday life. Think about a family where the parents have two different traits — say, one parent has curly hair and brown eyes, the other has straight hair and blue eyes. Their children might inherit any combination: curly hair with brown eyes, straight hair with blue eyes, curly hair with blue eyes, or straight hair with brown eyes. You can see that traits don’t always travel together; they can mix and match.
That mixing is exactly what a dihybrid cross is about. In biology, a dihybrid cross is a breeding experiment that tracks two different traits at the same time — for example, seed shape (round vs wrinkled) and seed colour (yellow vs green) in pea plants. The “dihybrid cross ratio” is the predictable pattern in which these two traits appear in the offspring when both parents are hybrid (carrying one dominant and one recessive version) for both traits.
The classic result, as stated in the NCERT textbook, is a 9:3:3:1 ratio in the second generation. That means:
- 9 out of 16 offspring show both dominant traits (e.g., round and yellow)
- 3 out of 16 show the first dominant trait and the second recessive trait (e.g., round and green)
- 3 out of 16 show the first recessive trait and the second dominant trait (e.g., wrinkled and yellow)
- 1 out of 16 shows both recessive traits (e.g., wrinkled and green)
The 9:3:3:1 ratio is not a random outcome. It is the direct consequence of independent assortment — the principle that genes for different traits are inherited independently of one another. This is one of Mendel’s key laws, and the ratio is its visible proof.
Why does this matter for a commerce or humanities student? Because this ratio is a classic example of probability in action. It shows how combinations of independent events produce predictable patterns — the same logic that underlies risk assessment in insurance, portfolio diversification in finance, or even the likelihood of certain combinations in a game of cards. You don’t need to calculate anything; you just need to see that nature follows rules, and those rules can be expressed as simple proportions. …
The bar graphs track a single trait (Tall vs Dwarf plant height), so they are monohybrid crosses. Cross I (all Tall) comes from TT x tt; Cross II (3:1) from Tt x Tt; Cross III (1:1) is a test cross (Tt x tt). Crosses I and II illustrate the Law of Dominance and the Law of Segregation.
Each graph plots the phenotypic proportion of the progeny for one character with two contrasting forms - Tall and Dwarf. Because only a single pair of contrasting traits is being followed, every one of these is a monohybrid cross (a dihybrid cross would follow two independent traits and give a 9:3:3:1 F2 ratio, which is not what these graphs show).
Genotypes of the parents
Cross I: the progeny are 100% Tall (Tall present, Dwarf absent). An all-tall progeny is obtained when a pure-breeding tall plant is crossed with a pure-breeding dwarf, TT x tt; every offspring is heterozygous (Tt) and therefore tall. (One parent is homozygous dominant, the other homozygous recessive.)
Cross II: the progeny appear in a 3 Tall : 1 Dwarf ratio. This is the defining monohybrid F2 ratio and is produced only when both parents are heterozygous, Tt x Tt. Each Tt parent forms T and t gametes in equal number; their random combination gives 1 TT : 2 Tt : 1 tt, i.e. 3 tall : 1 dwarf.
[OR variant of (a): the cross represented is a monohybrid cross - inheritance of one pair of contrasting characters (height).]
Concept understanding — Mendel's Law of Independent Assortment
Imagine you are packing two different suitcases for a trip. One suitcase is for clothes, the other for books. How you arrange the shirts inside the clothes suitcase has nothing to do with how you stack the books in the book suitcase. The two packing jobs happen independently.
That is the core intuition behind Mendel's Law of Independent Assortment. It says that when an organism passes on its genes to its offspring, the inheritance of one trait (like seed colour) does not influence the inheritance of another, separate trait (like seed shape). Each trait gets its own "lottery ticket" during reproduction, and the tickets are drawn separately.
The precise meaning
Gregor Mendel, working with pea plants in the 19th century, noticed that certain pairs of characteristics — for example, seed colour (yellow or green) and seed shape (round or wrinkled) — were inherited completely independently of each other. A plant could pass on a yellow colour gene and a wrinkled shape gene together, or a green colour and a round shape, or any combination. The chance of getting a particular colour was always 50-50 (in a certain cross), and the chance of getting a particular shape was also 50-50, and these chances did not affect each other.
The Law of Independent Assortment applies only to genes that are located on different chromosomes (or very far apart on the same chromosome). If two genes are on the same chromosome, they tend to be inherited together — that is called linkage, and it is an exception to this law. NCERT textbooks clearly state this limitation.
Why it matters
This law explains the enormous variety we see in living things. Because traits are shuffled independently, a single pair of parents can produce offspring with many different combinations of characteristics. For a human student, think of it this way: your eye colour and your hair colour are not tied together by fate. You could have your mother's eyes and your father's hair, or vice versa, or a mix. Independent assortment is one of the main reasons siblings (except identical twins) look different from each other.
In the NCERT Class 12 Biology textbook, Mendel's Law of Independent Assortment is stated as:
"When two pairs of traits are combined in a hybrid, segregation of one pair of characters is independent of the other pair of characters."
This means that during the formation of eggs and sperm (gametes), the alleles (versions of a gene) for one trait separate into gametes without being influenced by the alleles for another trait.
A few key points to remember
- It is the second law Mendel discovered (the first is the Law of Segregation, which says each organism has two copies of each gene and passes one copy randomly to offspring).
- It explains why a dihybrid cross (a cross involving two traits) yields a 9:3:3:1 ratio of offspring types — but you do not need to memorise that ratio for a prose subject. …
The bar graphs track a single trait (Tall vs Dwarf plant height), so they are monohybrid crosses. Cross I (all Tall) comes from TT x tt; Cross II (3:1) from Tt x Tt; Cross III (1:1) is a test cross (Tt x tt). Crosses I and II illustrate the Law of Dominance and the Law of Segregation.
Each graph plots the phenotypic proportion of the progeny for one character with two contrasting forms - Tall and Dwarf. Because only a single pair of contrasting traits is being followed, every one of these is a monohybrid cross (a dihybrid cross would follow two independent traits and give a 9:3:3:1 F2 ratio, which is not what these graphs show).
Cross III
Cross III gives a 1 Tall : 1 Dwarf ratio. A 1:1 progeny ratio is the hallmark of a test cross, in which an individual of the dominant phenotype but unknown genotype is crossed with the homozygous recessive: Tt x tt -> 50% Tt (tall) : 50% tt (dwarf). Its importance in genetics is that it lets us determine whether a dominant-looking individual is homozygous (TT) or heterozygous (Tt) - if any recessive (dwarf) offspring appear, the tested parent must be heterozygous.
Concept understanding — this question
Explanation coming soon.
The bar graphs track a single trait (Tall vs Dwarf plant height), so they are monohybrid crosses. Cross I (all Tall) comes from TT x tt; Cross II (3:1) from Tt x Tt; Cross III (1:1) is a test cross (Tt x tt). Crosses I and II illustrate the Law of Dominance and the Law of Segregation.
Each graph plots the phenotypic proportion of the progeny for one character with two contrasting forms - Tall and Dwarf. Because only a single pair of contrasting traits is being followed, every one of these is a monohybrid cross (a dihybrid cross would follow two independent traits and give a 9:3:3:1 F2 ratio, which is not what these graphs show).
Part (c) - Conclusion and principle …
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