JEE Main 2016MathematicsApplication of DerivativesMediumMCQ

JEE Main 2016 — Application of Derivatives Question with Solution

JEE Main 2016 (03 Apr)

Question

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side =x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then

Choose an option

Show full solutionCorrect option: A
Correct answer
Ax=2r

Step-by-step explanation




Given that 4x+2πr=2

i.e., 2x+πr=1

∴ r=1-2xπ .......(i)

Area A=x2+πr2

=x2+1π 2x-12

For min vale of area A

dAdx=0 gives x=2π+4 .......(ii)

From (i) and (ii)

r=1π+4 .......(iii)

∴ x=2r

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About this question

This is a previous-year question from JEE Main 2016, covering the Application of Derivatives 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.