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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 January 2020, Shift 1, Maths Q60

Question 60 of 75 in this shift, Maths question 10 of 25, Section A.

If ∫cos⁡x dxsin⁡3x (1+sin⁡6x)2/3=f(x) (1+sin⁡6x)1/λ+c\int\dfrac{\cos x\,dx}{\sin^3 x\,(1+\sin^6 x)^{2/3}}=f(x)\,(1+\sin^6 x)^{1/\lambda}+c where c is a constant of integration, then λf(π3)\lambda f\left(\frac{\pi}{3}\right) is equal to :
  1. (1)98\frac{9}{8}
  2. (2)−98-\frac{9}{8}
  3. (3)22
  4. (4)−2-2Official answer

Official answer

Option 4

NTA final key (Jan 2020).

Chapter
Integrals
Topic
Integration by Substitution
Idea tested
Factoring Highest Power for Substitution

Same idea in other shifts

Asked 3× in all
  1. 7 Apr 2025, Shift 2 · Q24If…HardNumerical value
  2. 26 Jun 2022, Shift 2 · Q28The integral 24π∫02(2−x2) dx(2+x2)4+x4\frac{24}{\pi}\int_0^{\sqrt{2}} \frac{(2 - x^2)\,dx}{(2 + x^2)\sqrt{4 + x^4}} is equal to ______.HardNumerical value

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.