JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 February 2021, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

Let

f(x)

be a differentiable function defined on [0, 2] such that

f'(x)=f'(2-x)

for all

x\in(0, 2)

f(0)=1

and

f(2)=e^2

. Then the value of

\int_{0}^{2}f(x)\,dx

is :

(1) $1-e^2$
(2) $1+e^2$ Official answer
(3) $2(1+e^2)$
(4) $2(1-e^2)$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: King's Property

Same idea in other shifts

Asked 18× 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.