JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2024, Shift 2, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let

\int_{\alpha}^{\log_e 4} \frac{dx}{\sqrt{e^x - 1}} = \frac{\pi}{6}

. Then

e^{\alpha}

and

e^{-\alpha}

are the roots of the equation :

(1) $x^2 + 2x - 8 = 0$
(2) $x^2 - 2x - 8 = 0$
(3) $2x^2 - 5x + 2 = 0$ Official answer
(4) $2x^2 - 5x - 2 = 0$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Exponential Factor Manipulation

Same idea in other shifts

Asked 4× 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.