JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q8

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

Let

f : \mathbf{R} \to \mathbf{R}

be a continuous function satisfying

f(x)+f(x+k)=n

, for all

x \in \mathbf{R}

where

k>0

and n is a positive integer. If

I_1=\int_0^{4nk} f(x)dx

and

I_2=\int_{-k}^{3k} f(x)dx

, then :

(1) $I_1+2I_2=4nk$
(2) $I_1+2I_2=2nk$
(3) $I_1+nI_2=4n^2k$ Official answer
(4) $I_1+nI_2=6n^2k$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Periodic Function Property

Same idea in other shifts

Asked 6× 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.