JEE Main 2022MathematicsContinuity and DifferentiabilityHardMCQ

JEE Main 2022 — Continuity and Differentiability Question with Solution

JEE Main 2022 (29 Jun Shift 1)

Question

Let f:R→R be a function defined by : fx=maxt≤xt3-3t;x≤2x2+2x-6;2<x<3x-3+9;3≤x≤52x+1; x>5
Where t is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and I=∫-22fxdx. Then the ordered pair m,I is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C4,274

Step-by-step explanation

fx=x3-3x,x≤-12,-1<x≤2x2+2x-6,2<x<39,3≤x<410,4≤x<511,x=52x+1,x>5

Clearly fx is not differentiable at x=2,3,4,5⇒m=4

I=∫-22fxdx=∫-2-1x3-3xdx+∫-122·dx=274

Hence the ordered pair is 4,274

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About this question

This is a previous-year question from JEE Main 2022, covering the Continuity and Differentiability 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.