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Saturday, 31 October

JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 5 April 2026, Shift 2, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let (21−a+21+a)(2^{1-a}+2^{1+a}), f(a)f(a), (3a+3−a)(3^a+3^{-a}) be in A.P. and α\alpha be the minimum value of f(a)f(a). Then the value of the integral ∫log⁡e(α−1)log⁡e(α)dx(e2x−e−2x)\int_{\log_e(\alpha-1)}^{\log_e(\alpha)}\frac{dx}{(e^{2x}-e^{-2x})} is :
  1. (1)12log⁡e(43)\frac{1}{2}\log_e\left(\frac{4}{3}\right)
  2. (2)14log⁡e(43)\frac{1}{4}\log_e\left(\frac{4}{3}\right)Official answer
  3. (3)12log⁡e(85)\frac{1}{2}\log_e\left(\frac{8}{5}\right)
  4. (4)14log⁡e(85)\frac{1}{4}\log_e\left(\frac{8}{5}\right)

Official answer

Option 2

NTA final key.

Chapter
Integrals
Topic
Integration by Substitution
Idea tested
Exponential Factor Manipulation

Same idea in other shifts

Asked 4× in all
  1. 8 Apr 2024, Shift 2 · Q11Let ∫αlog⁡e4dxex−1=π6\int_{\alpha}^{\log_e 4} \frac{dx}{\sqrt{e^x - 1}} = \frac{\pi}{6}. Then eαe^{\alpha} and e−αe^{-\alpha} are the roots of the…HardSingle correct
  2. 10 Apr 2023, Shift 2 · Q10For α,β,γ,δ∈N\alpha, \beta, \gamma, \delta \in \mathbb{N}, if…HardSingle correct
  3. 25 Jul 2022, Shift 1 · Q10The slope of the tangent to a curve C:y=y(x)C:y=y(x) at any point (x,y)(x,y) on it is…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.