Q.In a population of 1,000 individuals in Hardy-Weinberg equilibrium, a recessive allele a causes a metabolic disorder when present in the homozygous condition (aa). A population screening finds that 9% of individuals are affected. Calculate
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The Hardy–Weinberg principle describes the condition under which a population's allele and genotype frequencies remain constant across generations — i.e., a population that is genetically at equilibrium and therefore not evolving. For a gene with alleles A (frequency p) and a (frequency q), p + q = 1, and under random mating the next generation's genotype frequencies follow p2+2pq+q2=1, where p² is the frequency of AA, 2pq of Aa, and q² of aa. This equilibrium requires five simultaneous conditions: no mutation, random mating, no gene flow, an effectiv …
q²=0.09 ⇒ q=0.3, p=0.7; heterozygote (carrier) frequency 2pq = 2(0.7)(0.3) = 0.42 = 42%; number of carriers in 1,000 people = 420. …
Step 1. The affected (homozygous recessive, aa) frequency is given as 9% = 0.09 = q².
Step 2. Solve for q: q = √0.09 = 0.3.
Step 3. Since p + q = 1: p = 1 - 0.3 = 0.7.
Step 4. Heterozygote (carrier, Aa) frequency = 2pq = 2 × 0.7 × 0.3 = 0.42, i.e. 42%.
Step 5. Check: p² + 2pq + q² = 0.49 + 0.42 + 0.09 = 1.00. ✓ …
Take q² = the given homozygous-recessive frequency, take its square root for q, get p=1-q, then compute 2pq for the carrier fraction and multiply by population size for …
- Taking q = 0.09 directly instead of correctly taking the square root of 0.09 to get q=0.3.
- Forgetting to convert the carrier PERCENTAGE (42%) into an actual carrier COUNT (420) for …
- CBSE 2026Set ANNUAL1 markMCQQ.The factor which is essential for genetic equilibrium of allele frequencies in a population is(a) No mutation(b) genetic drift(c) gene flow(d) genetic recombination
›Reveal solutionSolution
Genetic equilibrium requires the absence of mutation (along with several other conditions), since mutation is one of the forces that changes allele frequencies.
The Hardy-Weinberg principle states that allele frequencies remain constant (in equilibrium) across generations only if a population is large, mates randomly, and is free from mutation, natural selection, migration (gene flow), and genetic drift. Among the given options, 'No mutation' is the essential condition listed for maintaining equilibrium, since mutation actively introduces new alleles or changes existing ones, thereby altering allele frequencies. Genetic drift (b) and gene flow (c) are themselves disturbing factors (not conditions …
- CBSE 2026Set SEM31 markMCQQ.Which of the following factors does not affect Hardy-Weinberg Principle ?(a) Gene flow(b) Mutation(c) Migration(d) Recapitulation
›Reveal solutionSolution
The Hardy-Weinberg principle holds when allele frequencies stay constant; it is disturbed by gene flow, genetic drift, mutation, migration, genetic recombination and natural selection. Recapitulation (a discredited embryological theory) is not one of these factors.
The Hardy-Weinberg principle states that allele and genotype frequencies (p² + 2pq + q² = 1) remain constant across generations in an ideal population. Equilibrium is disturbed by five/six evolutionary agencies: gene migration (gene flow), genetic drift, mutation, genetic recombination, and natural selection.
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- CBSE 2025Set 57/6/11 markMCQQ.If a natural population with 50 individuals is in Hardy-Weinberg equilibrium for a gene with two alleles A and a, with the gene frequency of allele A of 0·6, the genotype frequency of Aa will be : (A) 0·16 (B) 0·36 (C) 0·24 (D) 0·48
›Reveal solutionSolution
In a Hardy-Weinberg equilibrium population, the frequency of heterozygotes (Aa) is given by 2pq, which here equals 0.48.
To understand this question, you first need to recall the foundation of population genetics — the Hardy-Weinberg principle. This principle states that in a large, randomly mating population with no evolutionary forces acting (no mutation, migration, selection, or genetic drift), allele and genotype frequencies remain constant from generation to generation. The NCERT textbook presents this as a mathematical model where, for a gene with two alleles A and a, if the frequency of A is p and the frequency of a is q, then p + q = 1.
The genotype frequencies under equilibrium are given by the binomial expansion (p + q)² = p² + 2pq + q². Here, p² represents the frequency of AA homozygotes, 2pq represents the frequency of Aa heterozygotes, and q² represents the frequency of aa homozygotes.
In this problem, you are told that the population has 50 individuals and is in Hardy-Weinberg equilibrium. The frequency of allele A is given as 0.6. That means p = 0.6. Since p + q = 1, the frequency of allele a (q) must be 1 - 0.6 = 0.4.
Now, the question asks for the genotype frequency of Aa. According to the Hardy-Weinberg formula, this is 2pq. So you simply calculate:
2 × 0.6 × 0.4 = 0.48 …
- CBSE 2025Set X11 markMCQQ.If the change in gene frequency occurs by chance, it is called(a) Gene flow(b) Mutation(c) Genetic recombination(d) Genetic drift
›Reveal solutionSolution
A change in gene (allele) frequency occurring purely by chance is called genetic drift.
Genetic drift is the random change in allele frequencies in a population due to chance events, and it is especially significant in small populations. Gene flow is the movement of genes between populations through migration, mutation is a heritable change in the DNA sequence, and genet …
- CBSE 2025Set ANNUAL1 markQ.Define gene migration.
›Reveal solutionSolution
Gene migration is the transfer of alleles between populations through the movement of individuals, which alters the allele frequencies of the populations involved.
According to the Hardy-Weinberg principle, allele and genotype frequencies in a population remain constant (in equilibrium) generation after generation, provided certain conditions hold — no mutation, random mating, no natural selection, a large population size, and no gene migration. Gene migration (gene flow) is one of the factors that disturbs this equilibrium: when individuals move from one population into another (immigration) or leave a population (emigration), they carry their alleles with them. This changes the allele frequencies of both the population they leave and the population they join. If gene migration continues over generations between two populations, it …
- CBSE 2024Set 57/2/11 markMCQQ.A population is in genetic equilibrium/Hardy-Weinberg equilibrium for a gene with 2 alleles (dominant allele is 'A' and recessive allele 'a'). If the frequency of allele 'A' is 0·6, then the frequency of genotype 'Aa' is : (A) 0·21 (B) 0·42 (C) 0·48 (D) 0·32
›Reveal solutionSolution
The Hardy-Weinberg principle allows us to calculate genotype frequencies from allele frequencies in a stable population. Given the dominant allele frequency p = 0.6, the frequency of the heterozygous genotype 'Aa' is 0.48.
The question asks us to find the frequency of the heterozygous genotype 'Aa' in a population that is in genetic equilibrium, also known as Hardy-Weinberg equilibrium. This concept is fundamental to population genetics, as it describes a theoretical state where allele and genotype frequencies remain constant from generation to generation in the absence of evolutionary influences.
Concept and Intuition
The Hardy-Weinberg principle is a mathematical model that describes how genetic variation is maintained in a population under specific ideal conditions. These conditions include:
- No mutation
- No gene flow (migration)
- Random mating
- No genetic drift (large population size)
- No natural selection
When these conditions are met, the population is said to be in genetic equilibrium. For a gene with two alleles, typically denoted 'A' (dominant) and 'a' (recessive), we use specific symbols to represent their frequencies:
- Let p be the frequency of the dominant allele 'A'.
- Let q be the frequency of the recessive allele 'a'.
Since these are the only two alleles for this gene in the population, their frequencies must sum to 1:
p + q = 1
This equation represents the allele frequencies in the gene pool.
When individuals in this population mate randomly, the probability of forming different genotypes can be predicted. Imagine drawing two alleles at random from the gene pool to form a diploid individual.
- The probability of drawing 'A' and 'A' (forming 'AA') is p × p = p^2.
- The probability of drawing 'a' and 'a' (forming 'aa') is q × q = q^2.
- The probability of drawing 'A' and 'a' (forming 'Aa') is p × q.
- The probability of drawing 'a' and 'A' (forming 'aA') is q × p. Since 'Aa' and 'aA' represent the same heterozygous genotype, the total frequency of heterozygotes is pq + qp = 2pq.
Therefore, the frequencies of the three possible genotypes in the population must also sum to 1:
p^2 + 2pq + q^2 = 1
Here:
- p^2 represents the frequency of the homozygous dominant genotype 'AA'.
- 2pq represents the frequency of the heterozygous genotype 'Aa'.
- q^2 represents the frequency of the homozygous recessive genotype 'aa'. …
- CBSE 2024Set A11 markMCQQ.Which is the correct statement regarding Founder effect?(a) Named after the scientist John founder(b) No large change in frequency(c) The original drifted population become founders(d) Formation of no species
›Reveal solutionSolution
The founder effect is genetic drift in a small colonising group whose original drifted members become the founders of the new population.
When a few individuals establish a new colony, chance changes in allele frequency (genetic drift) can occur. Sometimes the change in allele frequency is so marked that the new sample of the population becomes a different species — the original drifted population becomes the founders and this is called the founder effect. …
- CBSE 2024Set ANNUAL1 markQ.________ principle says that allele frequencies in a population are stable and is constant from generation to generation.
›Reveal solutionSolution
The Hardy-Weinberg principle states that allele and genotype frequencies in a population remain constant (in equilibrium) generation after generation, in the absence of evolutionary forces.
According to the Hardy-Weinberg principle, allele frequencies in a population are stable/constant and remain in equilibrium from one generation to the next, provided the population is large, mating is random, and there is no mutation, migration, selection, or genetic drift. Summed allele fre …
- CBSE 2022Set ANNUAL1 markMCQQ.A population will not exist in Hardy Weinberg equilibrium, if :(a) There is no migration(b) Individuals mate selectively(c) The population is large(d) There are no mutations
›Reveal solutionSolution
Selective (non-random) mating violates one of the core assumptions of Hardy-Weinberg equilibrium, so the population will not remain in equilibrium.
The Hardy-Weinberg principle holds that allele and genotype frequencies in a population remain constant across generations only if several conditions are met: a very large population size (no genetic drift), no migration (gene flow) in or out, no mutation, random mating, and no natural selection acting on the alleles. Options (a) no migration, (c) large population, and (d) no mutations are all conditions that HELP maintain equilibrium, so they are not the answer. Selective (non-random) mating (b), however, means individuals preferentially choose mates based on certain traits/genotypes rather than mating randomly, whi …
- CBSE 2020Set ANNUAL1 markMCQQ.A population will not exist in Hardy-Weinberg equilibrium if :(a) The population is large.(b) Individuals mate selectively.(c) There are no mutations.(d) There is no migration.
›Reveal solutionSolution
Non-random (selective) mating is one of the classic factors that disrupts Hardy-Weinberg equilibrium.
The Hardy-Weinberg principle predicts that allele and genotype frequencies in a population remain constant across generations only if several idealised conditions hold: a very large population size (to avoid genetic drift), no mutation, no migration (gene flow), no natural selection, and random mating. If individuals mate selectively -- choosing mates based on particular traits rather than at random -- genotype frequencies shift away from Hardy-Weinberg expectations even without any change in allele frequency itself. The other three options (a large po …
- CBSE 2018Set ANNUAL1 markMCQQ.Transfer of gene between populations that differ genetically from one another is called ______.(a) Gene mutation(b) Gene flow(c) Genetic drift(d) Genetic recombination
›Reveal solutionSolution
(b) Gene flow — the movement of alleles/genes between genetically different populations via migration and interbreeding, one of the mechanisms driving evolutionary change.
Gene flow is the transfer of genes between populations by migration.
Gene flow (migration) occurs when individuals (or their gametes) move from one population to another and interbreed, introducing new alleles into the recipient population's gene pool and tending to reduce genetic differences between the two populations. This is distinct from gene mutation (a spontaneous change in the DNA sequence creating a new allele), genetic drift (random, chance fluctuations in allele frequency, especially significant in small populations), and genetic recombinatio …
- CBSE 2017Set ANNUAL1 markMCQQ.The collection of genes in a population is called :(a) gene pool(b) gene accumulation(c) gene population(d) genome
›Reveal solutionSolution
The sum total of genes/alleles in an interbreeding population is termed the gene pool.
The gene pool represents all the alleles of all genes carried by every individual in a population capable of interbreeding, and its allele frequencies form the basis for studying evolutionary change (e.g., via the Hardy-Weinberg principle). Changes in gene-pool composition over generations, due to mutation, selection, migration or genetic drift, constitute evolution at the population level. 'Genome' instead refers to the compl …
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