JEE Main 2013MathematicsDifferential EquationsMediumMCQ

JEE Main 2013 — Differential Equations Question with Solution

JEE Main 2013 (07 Apr)

Question

At present, a firm is manufacturing 2 00 0 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dPdx=100-12x. If the firm employs 2 5 more workers, then the new level of production of items is

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Show full solutionCorrect option: A
Correct answer
A3500

Step-by-step explanation

dPdx=100-12x

⇒∫dP=∫100-12xdx

⇒P=100x-8x3/2+C

Now, x=0

⇒P=2000⇒C=2000

hence, P=100x-8x32+2000

∵  x=25

P=2500-1000+2000

P=3500

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About this question

This is a previous-year question from JEE Main 2013, 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.