JEE Main 2014MathematicsDifferential EquationsMediumMCQ

JEE Main 2014 — Differential Equations Question with Solution

JEE Main 2014 (06 Apr)

Question

Let the population of rabbits surviving at a time t be governed by the differential equation dptdt=12{pt-400}. If p(0)=100, then p(t) equals 

Choose an option

Show full solutionCorrect option: C
Correct answer
C400 - 300 et/2

Step-by-step explanation

dptdt=12{pt-400}

p0=100

2dptpt-400=dt

Integrating,

⇒∫0p(t)dp(t)pt-400=∫0t12dt⇒lnpt-4000pt=t2

⇒lnpt-400300=t2

⇒pt-400=300et2

⇒400-pt=300et2    (∴pt<400)

⇒pt=400-300et2

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About this question

This is a previous-year question from JEE Main 2014, covering the Differential Equations chapter of Mathematics. 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.