JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 4 August 2021, Shift 1, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

I_1=\int_0^{\pi}xe^{\mathrm{cosec}\,x}dx

and

I_2=\int_0^{\pi}e^{\mathrm{cosec}\,x}dx

, then the ratio

I_1:I_2

is equal to

(1) $\pi:2$ Official answer
(2) $2:\pi$
(3) $\pi:3$
(4) $3:\pi$

Official answer

Option 1

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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5 Apr 2024, Shift 1 · Q10The value of $\int_{-\pi}^{\pi}\frac{2y(1+\sin y)}{1+\cos^2 y}\,dy$ is :MediumSingle correct
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1 Feb 2024, Shift 1 · Q10The value of the intergral $\int_0^{\pi/4}\frac{x\,dx}{\sin^4(2x)+\cos^4(2x)}$ equals :HardSingle correct
1 Feb 2024, Shift 2 · Q11The value of $\int_{-0}^{1}(2x^3-3x^2-x+1)^{\frac{1}{3}}\,dx$ is equal to :MediumSingle correct
27 Jan 2024, Shift 1 · Q12If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1, 2)$ , $(2, 3)$ and $(3, 1)$ , and $I_1=\int_a^b x\sin(4x-x^2)\,dx$ ,…HardSingle correct

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.