JEE Main 2019ChemistryChemical KineticsHardMCQ

JEE Main 2019 — Chemical Kinetics Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

A bacterial infection in an internal wound grows as N't=N0exp⁡(t) , where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as dNdt=-5N2 . What will be the plot of N0N vs t after 1 hour?

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Show full solutionCorrect option: A
Correct answer
A

Step-by-step explanation

From 0 to 1 hour, N'=N0et
From 1 hour onwards dNdt=-5N2
So at t=1 hour, N'=eN0
dNdt=-5N2
∫eN0NN-2dN=-5∫1tdt
1N-1eN0=5t-1
N0N-1e=5N0(t-1)
N0N=5N0(t-1)+1e
N0N=5N0t+1e-5N0
Which is following y=mx+C

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About this question

This is a previous-year question from JEE Main 2019, covering the Chemical Kinetics chapter of Chemistry. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.