The trap that costs marks here: confusing K-selected and r-selected species. NEET distractors routinely list humans or elephants as r-selected. They are K-selected — few offspring, high parental investment, long lifespan. Get the table straight, or you hand away a free mark.
Population attributes describe a population as a unit, not as individual organisms. Key attributes include birth rate (natality), death rate (mortality), sex ratio, and age distribution. NCERT Class 12 Biology Chapter 11, page 191 distinguishes these population-level parameters from individual traits. Age distribution is represented by age pyramids — expanding (high pre-reproductive proportion), stable, or declining (high post-reproductive proportion).
Growth models are where the formula lives. When resources are unlimited, a population grows exponentially:
dN/dt = rN
This is the J-shaped curve. But resources are never unlimited for long. The logistic growth model (Verhulst-Pearl) introduces carrying capacity K:
dN/dt = rN(K − N)/K
At small N, the term (K − N)/K ≈ 1, so growth is near-exponential. As N approaches K, the term approaches zero, and growth stalls — the S-shaped (sigmoid) curve. At N = K, dN/dt = 0: the population stabilises.
K-selected vs r-selected is a high-frequency confusion point. K-selected species (humans, elephants, whales) invest heavily in few offspring and live near carrying capacity. r-selected species (insects, weeds, many fish) produce many offspring with low survival rates and exploit empty niches. NEET distractors exploit the superficial similarity of the letters K and r to the growth equation's symbols.
Watch-out: when a question says "population growth is zero," it means N = K in the logistic model — not that the population is extinct.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
Which of the following is NOT a population attribute?
Answer: C. Phenotypic plasticity is an individual-level trait, not a population attribute. Population attributes include natality, mortality, sex ratio, and age distribution (NCERT Class 12 Biology Chapter 11, page 191).
Why A is wrong: A is wrong — natality (birth rate) is a fundamental population attribute described in NCERT Ch 12.
Why B is wrong: B is wrong — sex ratio is a population attribute that influences growth potential.
Why D is wrong: D is wrong — age distribution (represented as age pyramids) is a key population attribute.
In the logistic growth equation dN/dt = rN(K − N)/K, the letter K represents:
Answer: A. K is the carrying capacity — the maximum population size the environment can sustain indefinitely. This is defined in the Verhulst-Pearl logistic model (NCERT Class 12 Biology Chapter 11, page 195).
Why B is wrong: B is wrong — the intrinsic rate of natural increase is represented by 'r', not K.
Why C is wrong: C is wrong — initial population size is N₀ (or simply N at time zero); K is the upper limit the environment imposes.
Why D is wrong: D is wrong — there is no separate 'growth rate constant' in the logistic equation; r is the per capita rate and K is carrying capacity.
Which type of age pyramid indicates a declining population?
Answer: D. A declining population has more post-reproductive individuals than pre-reproductive ones, giving a narrow base and wider top — the urn shape (NCERT Class 12 Biology Chapter 11, page 191).
Why A is wrong: A is wrong — a broad base means a large pre-reproductive cohort, indicating an expanding population.
Why B is wrong: B is wrong — roughly equal proportions in all age classes indicates a stable population, not a declining one.
Why C is wrong: C is wrong — a bulging middle with moderate base suggests a stable or slowly growing population, not decline.
A bacterial population starts with N₀ = 100 cells and follows exponential growth with r = 0.5 per hour. Which equation correctly models its growth?
Answer: B. With unlimited resources (exponential growth), the integral form is Nt = N₀ × e^(rt). Substituting N₀ = 100 and r = 0.5 gives Nt = 100 × e^(0.5t). The logistic form (options A, C) applies only when carrying capacity limits growth (NCERT Class 12 Biology Chapter 11, pages 194–195).
Why A is wrong: A is wrong — this is the logistic model that includes carrying capacity K. The question specifies exponential (unlimited resource) growth, so no K term should appear.
Why C is wrong: C is wrong — this omits the N term entirely and incorrectly uses the logistic framework for what is stated as exponential growth.
Why D is wrong: D is wrong — this represents linear (arithmetic) growth, not exponential. Exponential growth involves multiplication by e^(rt), not addition of rt.
In the logistic growth model, at what population size is the rate of population increase (dN/dt) maximum?
Answer: C. In dN/dt = rN(K − N)/K, the product N(K − N) is maximised when N = K/2 (this is a standard quadratic optimisation). At N = K/2, the population is growing at its fastest rate. At N = K, growth is zero; at N near 0, growth is slow due to small population size (NCERT Class 12 Biology Chapter 11, pages 194–195).
Why A is wrong: A is wrong — at N = K, the factor (K − N) = 0, so dN/dt = 0. The population has reached carrying capacity and is no longer growing.
Why B is wrong: B is wrong — while (K − N)/K is near 1 when N is near 0, the factor N is also near zero, so the product rN(K − N)/K is negligible.
Why D is wrong: D is wrong — at N = K/4, dN/dt = r(K/4)(3K/4)/K = 3rK/16, which is less than the value at N = K/2 where dN/dt = rK/4 (= 4rK/16).
Which of the following is an example of a K-selected species?
Answer: A. Elephants are K-selected: large body size, few offspring per reproductive event, high parental investment, and long lifespan. The other three options — housefly, weeds, and mosquitoes — are r-selected: small body, many offspring, low parental investment (NCERT Class 12 Biology Chapter 11, page 196). This is a common confusion point where students misclassify large mammals as r-selected.
Why B is wrong: B is wrong — houseflies are r-selected (short lifespan, hundreds of eggs per batch, minimal parental care). (trap: mistake: k r selected)
Why C is wrong: C is wrong — Parthenium (a weed) is r-selected: rapid reproduction, massive seed output, colonises disturbed habitats. (trap: mistake: k r selected)
Why D is wrong: D is wrong — mosquitoes are r-selected: short generation time, large number of eggs, high mortality offset by sheer reproductive output. (trap: mistake: k r selected)
A population following logistic growth reaches N = K. A sudden environmental change then reduces K to K/2 while N remains unchanged. What happens to dN/dt immediately after the change?
Answer: B. After the change, N = K (original) but the new carrying capacity is K/2, so N > K_new. In the logistic equation, when N > K, the factor (K − N) is negative, making dN/dt negative. The population overshoots the new carrying capacity and must decline (NCERT Class 12 Biology Chapter 11, pages 194–195).
Why A is wrong: A is wrong — dN/dt = 0 only when N = K. After the change, N = K_old = 2 × K_new, so N ≠ K_new and dN/dt ≠ 0.
Why C is wrong: C is wrong — positive growth occurs when N < K. Here N > K_new, so the (K − N) term is negative, driving population decline, not growth.
Why D is wrong: D is wrong — the logistic equation is well-defined for all positive values of N, r, and K. There is no division by zero or indeterminate form here.
Two populations — Species X (insect, 10,000 offspring per clutch, short lifespan) and Species Y (mammal, 2 offspring per litter, long lifespan) — occupy the same habitat. After a catastrophic flood eliminates 90% of both populations, which species is expected to recover faster, and why?
Answer: B. Species X is r-selected with a high intrinsic rate of increase (r), enabling rapid reproduction and faster population recovery after a crash. K-selected Species Y reproduces slowly and takes longer to recover. The question tests understanding that r-selection is advantageous in unstable environments with frequent population crashes (NCERT Class 12 Biology Chapter 11, page 194). The distractors exploit the confusion between survival ability and reproductive recovery rate.
Why A is wrong: A is wrong — K-selected species invest in survival and competitive ability near carrying capacity, but their low reproductive rate means slower recovery after a population crash. Adaptation to survive catastrophe is not the same as ability to repopulate quickly. (trap: mistake: k r selected)
Why C is wrong: C is wrong — same habitat does not mean same reproductive strategy. Recovery rate depends on intrinsic rate of increase (r), which differs drastically between r-selected and K-selected species.
Why D is wrong: D is wrong — body size may affect individual survival during the flood, but the question asks about population recovery rate, which depends on reproductive output. Species Y's 2 offspring per litter cannot match Species X's 10,000 per clutch.
Get a structured 30-day study plan and a complete formula booklet — delivered to your inbox instantly.
Given
• K = 500 (carrying capacity, exact problem-defined value)• N = 250 (current population size, exact)• r = 0.1 per year (intrinsic rate of increase)
Required
dN/dt = ? (rate of population increase, individuals per year)
Concept
Logistic growth: population growth rate depends on both the current population size and how close it is to carrying capacity. Growth is fastest at N = K/2.
Formula
dN/dt = rN(K − N)/K
Substitution
dN/dt = 0.1 × 250 × (500 − 250) / 500
Calculation
dN/dt = 0.1 × 250 × 250 / 500
dN/dt = 0.1 × 250 × 0.5
dN/dt = 0.1 × 125
dN/dt = 12.5 individuals per year
Note on exact values: K = 500, N = 250 are exact counting/problem-defined integers. They do not limit significant figures. The result precision is governed by r = 0.1 (1 significant figure by strict rules, but conventionally treated as exact in NCERT-style biology problems where r is a given parameter).
Final answer
dN/dt = 12.5 individuals per year
This is the maximum possible growth rate for this population because N = 250 = K/2, which is exactly the inflection point of the sigmoid curve.
Common trap
Students sometimes substitute into the exponential model (dN/dt = rN = 0.1 × 250 = 25) and forget the logistic correction factor (K − N)/K. The logistic factor halves the answer here because N/K = 0.5. Always check whether the problem specifies limited resources or carrying capacity — if yes, use the logistic equation.
Similar NEET-style question
A population of 200 organisms follows logistic growth with r = 0.2 per year and K = 800. Calculate dN/dt and determine whether this population is at, below, or above the inflection point of growth.
*(Answer: dN/dt = 0.2 × 200 × 600/800 = 30 individuals/year. Since N = 200 < K/2 = 400, the population is below the inflection point and growth rate is still increasing.)*
---
Exponential: dN/dt = rN; J-shaped curve. Logistic: dN/dt = rN(K-N)/K; sigmoid (S) curve. K = carrying capacity. r-selected (high r, small body, semelparous) vs K-selected (low r, large body, iteroparous).
-- NCERT Class 12 Biology, Chapter 11, p. 194Population grows exponentially at small N; growth slows as N approaches K (carrying capacity); equilibrium at N = K.
| Symbol | Quantity | SI Unit |
|---|---|---|
| N | population size | - |
| r | intrinsic rate of increase | /time |
| K | carrying capacity | - |
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Root cause: term confusion
K-selected: large body, few offspring with high parental investment, long-lived (whales, humans, elephants). r-selected: small body, many offspring, low investment, short-lived (insects, weeds).
More in Ecology and Environment: 2 exam traps and mistakes · 2 formulas · 1 question pattern from its other lessons.
8 questions from NEET 2020, 2021, 2022, 2023, 2024, 2025, 2026. Answers verified against NTA official keys.
Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?
In the exponential growth equation Nt = Noert, e represents
Which of the following is not an attribute of a population ?
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
Test yourself on this topic with real past-paper questions:
Practice this topic →