JEE Main 2022 · MathsMultiple choiceTwo statementsMediumMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

Let

f(x) = 2 + |x| - |x - 1| + |x + 1|

x \in \mathbf{R}

. Consider (S1) :

f'\left(-\frac{3}{2}\right) + f'\left(-\frac{1}{2}\right) + f'\left(\frac{1}{2}\right) + f'\left(\frac{3}{2}\right) = 2

(S2) :

\int_{-2}^{2} f(x)\,dx = 12

Then,

(1)both (S1) and (S2) are correct
(2)both (S1) and (S2) are wrong
(3)only (S1) is correct
(4)only (S2) is correctOfficial answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Differentiability of Modulus Functions

Same idea in other shifts

Asked 9× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.