JEE Main 2022MathematicsContinuity and DifferentiabilityMediumMCQ

JEE Main 2022 — Continuity and Differentiability Question with Solution

JEE Main 2022 (28 Jun Shift 1)

Question

Let f:ℝ→ℝ be defined as fx=ex,x<0aex+x-1,0≤x<1b+sinπx,1≤x<2e-x-c,x≥2
where a,b,c∈ℝ and t denotes greatest integer less than or equal to t. Then, which of the following statements is true?

Choose an option

Show full solutionCorrect option: C
Correct answer
CIf f is discontinuous at exactly one point, then a+b+c≠1.

Step-by-step explanation

Given fx=ex,x<0aex+x-1,0≤x<1b+sinπx,1≤x<2e-x-c,x≥2

i.e. fx=0,x<0aex-1,0≤x<1b,x=1b-1,1<x<2-c,x≥2

Here, we know fx is discontinuous at x=1 as b≠b-1

For fx to be continuous at x=0; a=1

For fx to be continuous at x=2; b+c=1

Hence, a+b+c=2

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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.