NEET · Biology · STD 12 - 11. organisms and populations

Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?

A \(\frac{d N}{d t}=r\left(\frac{K-N}{K}\right)\)
B \(\frac{d N}{d t}=r N\left(\frac{K-N}{K}\right)\)
C \(\frac{d N}{d t}=r N\left(\frac{N-K}{N}\right)\)
D \(\frac{d N}{d t}=N\left(\frac{r-K}{K}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{d N}{d t}=r N\left(\frac{K-N}{K}\right)\)

Step-by-step Solution

Detailed explanation

Logistic growth is described by Verhulst-Pearl logistic growth equation \(\frac{d N}{d t}=r N\left(\frac{K-N}{K}\right)\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the following events that occur in their respective phases of cell cycle and select the correct option :

Column \(I\)	Column \(II\)
(\(a\)) \(G _{1}\) phase	(\(i\)) Cell grows and organelle duplication
(\(b\)) \(S\) phase	(\(ii\)) \(DNA\) replication and chromosome duplication
(\(c\)) \(G _{2}\) phase	(\(iii\)) Cytoplasmic growth
(\(d\)) Metaphase in \(M\)-phase	(\(iv\)) Alignment of chromosomes

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