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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 August 2021, Shift 1, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

Let f(x)=cos⁡(2tan⁡−1sin⁡(cot⁡−11−xx))f(x) = \cos\left(2\tan^{-1}\sin\left(\cot^{-1}\sqrt{\frac{1-x}{x}}\right)\right), 0<x<10 < x < 1. Then :
  1. (1)(1−x)2f′(x)−2(f(x))2=0(1-x)^2 f'(x) - 2(f(x))^2 = 0
  2. (2)(1+x)2f′(x)+2(f(x))2=0(1+x)^2 f'(x) + 2(f(x))^2 = 0
  3. (3)(1−x)2f′(x)+2(f(x))2=0(1-x)^2 f'(x) + 2(f(x))^2 = 0Official answer
  4. (4)(1+x)2f′(x)−2(f(x))2=0(1+x)^2 f'(x) - 2(f(x))^2 = 0

Official answer

Option 3

NTA final key.

Same idea in other shifts

Asked 2× in all
  1. 9 Apr 2024, Shift 2 · Q11The integral ∫1/43/4cos⁡(2cot⁡−11−x1+x)dx\int_{1/4}^{3/4}\cos\left(2\cot^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx is equal toMediumSingle 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.