Solved Examples — Class 12 Biology Notes

Section 14 — Solved Examples

Welcome to the dedicated problem set for Chapter 6 (Evolution). The 32 worked examples below are arranged in three tiers — concept checks (origin of life, the theories, the evidences), application & scenarios (adaptive radiation, industrial melanism, resistance, types of selection) and analytical & multi-concept (Hardy–Weinberg calculations, the geological timeline and integrated reasoning).

Use this as a last-mile revision tool. Most of these are deliberately not plain definitions — they ask you to reason, compare and calculate, because that is where Board and NEET marks are won in this chapter. The Hardy–Weinberg numeric problems in particular repay careful practice: learn to spot $q^2$ in a word problem and the rest of the algebra falls out on its own.

How to use this section

Concept Checks (Q1–Q10): If you can't answer 9/10 quickly, revisit Sections 1–5 (for Q9–Q10, Sections 9–10).
Application & Scenarios (Q11–Q22): The bread-and-butter of 2- and 3-mark questions — radiation, melanism, resistance, selection types.
Analytical & Multi-Concept (Q23–Q32): Multi-step reasoning and Hardy–Weinberg sums that string several ideas together.

Total target time: ~60 minutes for a full revision sweep.

Note: This section is for practice and revision only — there is no quiz at the end. Pair it with Section 15 (Board Exam-Pattern Questions) and Section 16 (NEET-Pattern Practice Questions).

Memory Capsule — Top Patterns to Master

Before you dive in, lock these 10 high-yield patterns in your head:

#	Pattern / Fact	Where it's tested
1	Lamarck: use/disuse + inheritance of acquired characters (giraffe's neck)	Theory comparison
2	Darwin (with Wallace): variation + natural selection → reproductive fitness; branching descent from a common ancestor; Malthus' idea of over-reproduction	Theory questions
3	Homology = divergent = common ancestry (forelimbs); analogy = convergent = same function, different origin (bird vs butterfly wing)	Evidence sorting
4	Adaptive radiation: one ancestor → many forms in a new area (Darwin's finches, Australian marsupials); same area twice = convergent	Radiation problems
5	Industrial melanism: light moths → dark moths with soot (lichen dies, dark moths hidden, light ones eaten)	Selection in action
6	de Vries: evolution by sudden mutation / saltation (evening primrose), not Darwin's slow steps	Mechanism questions
7	Selection types: stabilising → mean favoured; directional → one extreme; disruptive → both extremes	Graph/scenario reading
8	Hardy–Weinberg: $p + q = 1$ and $p^2 + 2pq + q^2 = 1$ ; recessive phenotype = $q^2$ → root for $q$	Numeric sums
9	5 factors that disturb equilibrium: gene flow, genetic drift, mutation, recombination, natural selection (+ founder effect)	Equilibrium logic
10	Timeline anchors: cells ~2000 mya, invertebrates ~500 mya, jawless fish ~350 mya, dinosaurs vanish 65 mya; man: Australopithecus ~2 mya → sapiens 75,000–10,000 yrs	Sequence/date questions

Pro tip: For any Hardy–Weinberg word problem, find $q^2$ first (usually the recessive phenotype), then $q = \sqrt{q^2}$ , then $p = 1 - q$ , and every other frequency follows.

Concept Checks (Q1–Q10)

Q1. How does Lamarck explain the long neck of the giraffe, and what is the fatal flaw in his reasoning?

Answer: Lamarck said ancestors stretched their necks to reach high leaves (use), and this acquired length was passed to offspring. The flaw is that characters gained during an individual's lifetime are not inherited — the germ cells are unchanged — so use and disuse cannot drive evolution.

Q2. Darwin and Wallace independently reached the same theory. What was its central mechanism, and whose idea of over-reproduction inspired it?

Answer: The mechanism is natural selection: individuals vary, more are born than can survive, and those better suited leave more offspring (reproductive fitness), so favourable variations spread. The idea that populations reproduce faster than resources allow came from Malthus.

Q3. Why are fossils called direct or palaeontological evidence for evolution, and how is their age worked out?

Answer: Fossils are the preserved remains or impressions of organisms that lived long ago, so they show past life-forms directly. Their age is estimated from the rock layer they lie in and by radioactive (radiometric) dating of the surrounding rock.

Q4. Forelimbs of a whale, a bat and a human have the same bone plan but do very different jobs. What are such organs called, and what do they prove?

Answer: They are homologous organs. The shared internal design points to a common ancestor whose limb was modified for different uses — this is divergent evolution.

Q5. The wing of a bird and the wing of a butterfly both allow flight but are built quite differently. What term describes them, and what kind of evolution do they illustrate?

Answer: They are analogous organs — same function, different structure and origin. They arise by convergent evolution, where unrelated groups meet a similar need in similar-looking ways.

Q6. What did Haeckel and von Baer contribute to the embryological evidence for evolution?

Answer: Haeckel noticed that early embryos of different vertebrates look strikingly alike and proposed embryos repeat ancestral stages. von Baer later showed embryos never pass through the adult stages of other animals — they share only early features, which still points to common ancestry.

Q7. Define adaptive radiation and give one classic example.

Answer: Adaptive radiation is the evolution of many different species from a single ancestral form when it enters a new area with varied conditions. The classic example is Darwin's finches on the Galapagos, which radiated into forms with different beaks for different foods.

Q8. How does de Vries' idea of how new species arise differ from Darwin's?

Answer: de Vries said evolution proceeds by large, sudden mutations (saltation) that create a new species in one step — he saw this in the evening primrose. Darwin held that evolution is slow and gradual, built from small variations selected over many generations.

Q9. Name the three types of natural selection by what part of a trait's distribution they favour.

Answer: Stabilising selection favours the mean (average) and removes both extremes; directional selection favours one extreme, shifting the mean; disruptive selection favours both extremes and works against the mean.

Q10. Write the two Hardy–Weinberg equations and state what each symbol means.

Answer: $p + q = 1$ and $p^2 + 2pq + q^2 = 1$ . Here $p$ is the frequency of the dominant allele and $q$ that of the recessive allele; $p^2$ is the frequency of homozygous dominants ( $AA$ ), $q^2$ of homozygous recessives ( $aa$ ), and $2pq$ of heterozygotes ( $Aa$ ).

Application & Scenarios (Q11–Q22)

Q11. In an area with heavy industrial soot, the peppered moth population shifted from mostly light to mostly dark forms. Walk through why, using predation and lichen.

Answer: Soot killed the pale lichen on tree bark and blackened it. On dark bark, light moths were now conspicuous and eaten by birds, while dark moths were camouflaged and survived to breed. Selection therefore favoured the dark form — a case of directional selection (industrial melanism) seen within a few decades.

Q12. The same peppered moths were pale before industrialisation. Predict what would happen to the moth population if pollution were cleaned up and lichen returned.

Answer: With clean, lichen-covered bark, light moths become well camouflaged and dark moths stand out and are eaten. Selection would swing back the other way, and the light form would once again become common — showing selection tracks the environment.

Q13. A patient stops a course of antibiotics early and the infection returns, now harder to treat. Explain this in evolutionary terms.

Answer: The population contained a few bacteria with resistance variations. The antibiotic killed the susceptible majority but the resistant few survived and multiplied, so the surviving population is now largely resistant. This is natural selection driven by human activity (anthropogenic selection), and it happens fast because bacteria reproduce quickly.

Q14. Australia has a marsupial 'wolf' and other continents have a placental wolf that look and hunt alike, yet they are not close relatives. What does this show, and what is it called?

Answer: Living in similar niches, unrelated marsupial and placental mammals evolved similar body forms and habits independently. This is convergent evolution; because it happened across separate radiations, it is sometimes called convergent (adaptive) radiation.

Q15. Sweet potato tubers and potato tubers both store food underground, but one is a modified root and the other a modified stem. Are they homologous or analogous? Justify.

Answer: They are analogous — same function (storage) but different origins (root vs stem). Similarity of function without shared structural origin is analogy, produced by convergent evolution, not common ancestry.

Q16. The eye of an octopus and the eye of a mammal are remarkably alike in working design, though the animals are only distantly related. Classify this and name the process.

Answer: These are analogous organs: two lineages arrived at a similar camera-type eye independently. The process is convergent evolution, where similar selection pressures produce similar solutions in unrelated groups.

Q17. A penguin's flipper and a dolphin's flipper both power swimming. Are they homologous or analogous, and what evolution do they show?

Answer: As paddle-shaped swimming limbs they are analogous in function; a bird and a mammal reaching the same streamlined shape for life in water is convergent evolution. (Their internal bones, being modified vertebrate forelimbs, are homologous — but the flipper shape is the convergent, analogous feature.)

Q18. A body height distribution in a stable environment loses its very tall and very short individuals over generations, leaving most people near the average. Which type of selection is this, and what happens to the mean?

Answer: This is stabilising selection — the extremes are selected against and the average (mean) is favoured. The mean stays the same while variation around it is reduced.

Q19. In a population of seed-eating birds, only birds with very small beaks or very large beaks feed well, while medium beaks starve. Which selection type is this, and what is the long-term outcome?

Answer: This is disruptive selection — both extremes are favoured and the intermediate is selected against. Over time it can split the population into two distinct groups (large-beaked and small-beaked), a starting point for the formation of new species.

Q20. List the five factors that can disturb Hardy–Weinberg equilibrium, and add the special case that occurs when a small group founds a new population.

Answer: The five are gene flow (migration), genetic drift, mutation, recombination and natural selection. The special case is the founder effect — a few individuals starting a new population carry only a sample of the original alleles, so the new population's frequencies differ from the parent's (a form of drift).

Q21. A small group leaves a large population and colonises an island; by chance they carry an unusually high frequency of a rare allele. Name the effect and the general process it belongs to.

Answer: This is the founder effect, a case of genetic drift — random change in allele frequency that is strong in small populations. The island population's gene pool now differs from the parent population simply by the luck of who happened to migrate.

Q22. Arrange these milestones in the correct order and give an approximate date for each: first cells, first invertebrates, jawless fish, extinction of dinosaurs.

Answer: First cells ~2000 mya → first invertebrates ~500 mya → jawless fish ~350 mya → dinosaurs disappear ~65 mya. Life began in water with single cells, invertebrates and then fish followed, and the dinosaurs vanished about 65 million years ago, after which mammals rose to dominance.

Analytical & Multi-Concept (Q23–Q32)

Q23. In a population at equilibrium, a recessive disorder ( $aa$ ) appears in 9% of individuals. Find (a) $q$ , (b) $p$ , (c) the frequency of carriers, and (d) the frequency of homozygous dominants.

Answer: $q^2 = 0.09$ , so (a) $q = \sqrt{0.09} = 0.3$ . (b) $p = 1 - 0.3 = 0.7$ . (c) carriers $= 2pq = 2 \times 0.7 \times 0.3 = 0.42$ (42%). (d) $p^2 = 0.49$ (49%). Check: $0.49 + 0.42 + 0.09 = 1$ . ✓

Q24. In a Hardy–Weinberg population the recessive phenotype has a frequency of 16%. Calculate the frequencies of the dominant allele, the heterozygotes and the homozygous dominants.

Answer: $q^2 = 0.16 \Rightarrow q = 0.4$ , so $p = 1 - 0.4 = 0.6$ . Heterozygotes $= 2pq = 2 \times 0.6 \times 0.4 = 0.48$ (48%); homozygous dominants $= p^2 = 0.36$ (36%). Check: $0.36 + 0.48 + 0.16 = 1$ . ✓

Q25. In a population the recessive allele frequency is $q = 0.2$ . Without measuring phenotypes, predict the frequencies of $AA$ , $Aa$ and $aa$ individuals.

Answer: $p = 1 - 0.2 = 0.8$ . Then $AA = p^2 = 0.64$ (64%), $Aa = 2pq = 2 \times 0.8 \times 0.2 = 0.32$ (32%), $aa = q^2 = 0.04$ (4%). Check: $0.64 + 0.32 + 0.04 = 1$ . ✓

Q26. A recessive trait affects 1 in 10,000 people. Assuming equilibrium, estimate the frequency of carriers (heterozygotes) in the population.

Answer: $q^2 = 1/10000 = 0.0001$ , so $q = 0.01$ and $p = 1 - 0.01 = 0.99$ . Carriers $= 2pq = 2 \times 0.99 \times 0.01 = 0.0198$ , i.e. about 0.02 (roughly 1 in 50 people carries the allele) — far more common than the affected, which is why recessive alleles persist.

Q27. In a population of 500 individuals at equilibrium, the dominant allele frequency is $p = 0.6$ . How many individuals of each genotype ( $AA$ , $Aa$ , $aa$ ) are expected?

Answer: $q = 0.4$ . Frequencies: $AA = p^2 = 0.36$ , $Aa = 2pq = 0.48$ , $aa = q^2 = 0.16$ . Numbers out of 500: $AA = 0.36 \times 500 = 180$ , $Aa = 0.48 \times 500 = 240$ , $aa = 0.16 \times 500 = 80$ . Check: $180 + 240 + 80 = 500$ . ✓

Q28. A survey of 2000 people finds 80 with a recessive condition. Using Hardy–Weinberg, estimate the frequency of the recessive allele and the number of carriers.

Answer: $q^2 = 80/2000 = 0.04$ , so $q = 0.2$ and $p = 0.8$ . Carrier frequency $= 2pq = 2 \times 0.8 \times 0.2 = 0.32$ ; number of carriers $= 0.32 \times 2000 = 640$ people. So the recessive allele frequency is 0.2 and about 640 carriers are expected.

Q29. A biologist measures the genotype frequencies in a wild population and finds they do not match the values predicted by $p^2 + 2pq + q^2 = 1$ . What does this tell her, and why?

Answer: It tells her the population is not in genetic equilibrium — its allele frequencies are changing from generation to generation. Since a change in allele frequency over time is the definition of evolution, the gap between observed and expected values is a measure of evolution in progress, driven by one or more of the five factors.

Q30. Sort these into homology vs analogy and name the evolution shown by each: (i) forelimbs of whale, bat and human; (ii) wings of bird and insect; (iii) sweet potato (root) and potato (stem).

Answer: (i) Vertebrate forelimbs — same bone plan, different jobs — are homologous → divergent evolution → common ancestry. (ii) Bird and insect wings — same function, different build — are analogous → convergent evolution. (iii) Storage root vs storage stem — same function, different origin — are analogous → convergent evolution.

Q31. Two suspects in the story of evolution: Lamarck and Darwin both explained the giraffe's neck. Compare their explanations and state which is accepted, and why.

Answer: Lamarck: ancestors stretched their necks (use) and passed the acquired length on — but acquired traits are not inherited, so this fails. Darwin: giraffes varied in neck length; those with longer necks reached more food, survived and left more offspring (natural selection), so the trait spread. Darwin's explanation is accepted, because it relies on heritable variation and differential reproductive success rather than inheritance of acquired characters.

Q32. Master integrative question. A population of moths lives on lichen-covered bark and is 95% light-coloured. Industrial soot then blackens the bark for 40 years, after which the area is cleaned and lichen returns.

(a) What type of selection acts during the soot years, and on which form? (b) What happens to allele frequencies during that time, and does it satisfy Hardy–Weinberg? (c) Predict the population after the clean-up.

Answer:

(a) Directional selection favouring the dark (melanic) form, because on soot-blackened bark light moths are eaten by birds and dark moths are camouflaged.

(b) The frequency of the dark allele rises and the light allele falls across generations. Because allele frequencies are changing, the population is not at Hardy–Weinberg equilibrium — natural selection is one of the five disturbing factors, and this shift is evolution in action.

(c) After clean-up, lichen returns and pale bark again favours the light form; birds now eat the conspicuous dark moths. Selection reverses direction and the light form becomes common once more — showing that selection has no fixed goal but simply tracks the current environment.

End of Section 14

You have now worked through 32 examples spanning the origin of life, Lamarck and Darwin, the evidences (fossils, homology, analogy, embryology), adaptive radiation, industrial melanism and resistance, de Vries' mutation theory, the three types of selection, Hardy–Weinberg calculations and the geological timeline. For more sustained practice, move on to Section 15 (Board Exam-Pattern Questions) and Section 16 (NEET-Pattern Practice Questions).

Self-assessment: Aim for 24 / 32 correct on a first attempt. If you struggled with the Hardy–Weinberg sums (Q23–Q28), redo Section 10 until finding $q^2$ and taking its square root is automatic — those numeric problems are among the most reliable marks in the whole chapter.