Which one of the given equations is related to Hardy-Weinberg equilibrium?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → p2 + 2pq + q2 =1
The Hardy-Weinberg principle says that the frequencies of alleles in a population stay the same from one generation to the next, when no evolutionary force acts on it. In a gene with two alleles, p is the frequency of one allele (A) and q is the frequency of the other allele (a).
(1) p + q=2 — Incorrect. The frequencies of the two alleles together make the whole gene pool, so p + q = 1. They can never add up to 2.
(2) p2 + 2pq + q2 =1 — Correct. A diploid individual carries two alleles, so the genotype frequencies are p2 for AA, 2pq for Aa and q2 for aa. All three genotypes together make the whole population, so they add up to 1. This is the binomial expansion of (p + q)2.
(3) p2 + q2 =1 — Incorrect. This leaves out the heterozygotes (Aa), which have the frequency 2pq. The sum would then be less than 1.
(4) p2 + q2 =2pq — Incorrect. The frequency of the heterozygotes is not equal to the frequency of the two homozygotes together. This is not a Hardy-Weinberg equation.
Note: A similar question was also asked in CUET (UG) 2026 on 29-05-2026 (Slot 1).
NCERT Extract:
Hardy-Weinberg Principle – “… The frequency of AA individuals in a population is simply p2. This is simply stated in another ways, i.e., the probability that an allele A with a frequency of p appear on both the chromosomes of a diploid individual is simply the product of the probabilities, i.e., p2. Similarly of aa is q2, of Aa 2pq. Hence, p2+2pq+q2=1. This is a binomial expansion of (p+q)2.”