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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

If ∫cos⁡x−sin⁡x8−sin⁡2xdx=asin⁡−1(sin⁡x+cos⁡xb)+c\int \frac{\cos x - \sin x}{\sqrt{8 - \sin 2x}}dx = a\sin^{-1}\left(\frac{\sin x + \cos x}{b}\right) + c, where c is a constant of integration, then the ordered pair (a, b) is equal to :
  1. (1)(3,1)(3, 1)
  2. (2)(1,3)(1, 3)Official answer
  3. (3)(−1,3)(-1, 3)
  4. (4)(1,−3)(1, -3)

Official answer

Option 2

NTA final key.

Chapter
Integrals
Topic
Integration by Substitution
Idea tested
sin(2x) Derivative 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. 5 Apr 2024, Shift 1 · Q11The integral ∫0π/4136sin⁡x3sin⁡x+5cos⁡x dx\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx is equal to :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 108 of the 174 JEE Main shifts held from 2017 to 2026.