JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

\int_0^1\frac{1}{\left(5+2x-2x^2\right)\left(1+e^{(2-4x)}\right)}dx=\frac{1}{\alpha}\log_e\left(\frac{\alpha+1}{\beta}\right)

\alpha,\beta>0

, then

\alpha^4-\beta^4

is equal to

(1) $-21$
(2) $0$
(3) $19$
(4) $21$ Official answer

Official answer

Option 4

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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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
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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.