JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

\int_0^{100\pi}\frac{\sin^2x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}}dx=\frac{\alpha\pi^3}{1+4\pi^2}

\alpha\in\mathbf{R}

, where

[x]

is the greatest integer less than or equal to

x

, then the value of

\alpha

is :

(1) $150\,(e^{-1}-1)$
(2) $50\,(e-1)$
(3) $100\,(1-e)$
(4) $200\,(1-e^{-1})$ Official answer

Official answer

Option 4

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.