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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

For x∈(−π2,π2)x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right), if y(x)=∫cosec x+sin⁡xcosec xsec⁡x+tan⁡xsin⁡2xdxy(x)=\int\frac{\mathrm{cosec}\,x+\sin x}{\mathrm{cosec}\,x\sec x+\tan x\sin^2x}dx, and lim⁡x→(π2)−y(x)=0\lim_{x\to\left(\frac{\pi}{2}\right)^-}y(x)=0 then y(π4)y\left(\frac{\pi}{4}\right) is equal to
  1. (1)tan⁡−1(12)\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)
  2. (2)12tan⁡−1(−12)\frac{1}{\sqrt{2}}\tan^{-1}\left(-\frac{1}{2}\right)Official answer
  3. (3)−12tan⁡−1(12)-\frac{1}{\sqrt{2}}\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)
  4. (4)12tan⁡−1(12)\frac{1}{2}\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)

Official answer

Option 2

NTA final key.

Chapter
Integrals
Topic
Integration by Substitution
Idea tested
Odd Power of Cosine Substitution

Same topic in other shifts

All Integration by Substitution questions
  1. 5 Apr 2026, Shift 1 · Q20The value of the integral ∫π/6π/3(4−cosec⁡2xcos⁡4x)dx\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx is:MediumSingle correct
  2. 5 Apr 2026, Shift 2 · Q18Let (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…HardSingle correct
  3. 3 Apr 2025, Shift 1 · Q18Let f(x)=∫x33−x2 dxf(x) = \int x^3\sqrt{3 - x^2}\,dx. If 5f(2)=−45f(\sqrt{2}) = -4, then f(1)f(1) is equal toMediumSingle correct
  4. 4 Apr 2025, Shift 2 · Q25If…HardNumerical value
  5. 7 Apr 2025, Shift 2 · Q24If…HardNumerical value
  6. 6 Apr 2024, Shift 2 · Q12If ∫1a2sin⁡2x+b2cos⁡2xdx=112tan⁡−1(3tan⁡x)+constant\int\frac{1}{a^2\sin^2x+b^2\cos^2x}dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}, then the maximum value of asin⁡x+bcos⁡xa\sin x+b\cos x, is :MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.