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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardConceptual

JEE Main 17 March 2021, Shift 1, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

Which of the following statements is incorrect for the function g(α)g(\alpha) for α∈R\alpha\in\mathbf{R} such that g(α)=∫π/6π/3sin⁡αxcos⁡αx+sin⁡αx dxg(\alpha)=\int_{\pi/6}^{\pi/3}\frac{\sin^{\alpha}x}{\cos^{\alpha}x+\sin^{\alpha}x}\,dx
  1. (1)g(α)g(\alpha) is a strictly increasing function
  2. (2)g(α)g(\alpha) is a strictly decreasing function
  3. (3)g(α)g(\alpha) has an inflection point at α=−12\alpha=-\frac{1}{2}
  4. (4)g(α)g(\alpha) is an even function

Official answer

Dropped by NTA (marks given to all)

NTA final key: NTA final key 'D' = question dropped.

Chapter
Integrals
Topic
Definite Integral Properties
Idea tested
King's Property

Same idea in other shifts

Asked 18× in all
  1. 3 Apr 2025, Shift 2 · Q18The integral ∫0π8x dx4cos⁡2x+sin⁡2x\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x} is equal toMediumSingle correct
  2. 8 Apr 2025, Shift 2 · Q18Let f(x)f(x) be a positive function and I1=∫−1212x f(2x(1−2x)) dxI_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx and…HardSingle correct
  3. 4 Apr 2024, Shift 1 · Q25If ∫0π/4sin⁡2x1+sin⁡xcos⁡xdx=1alog⁡e(a3)+πb3\int_0^{\pi/4}\frac{\sin^2x}{1+\sin x\cos x}dx=\frac{1}{a}\log_e\left(\frac{a}{3}\right)+\frac{\pi}{b\sqrt{3}}, where…HardNumerical value
  4. 5 Apr 2024, Shift 1 · Q10The value of ∫−ππ2y(1+sin⁡y)1+cos⁡2y dy\int_{-\pi}^{\pi}\frac{2y(1+\sin y)}{1+\cos^2 y}\,dy is :MediumSingle correct
  5. 5 Apr 2024, Shift 2 · Q25If f(t)=∫0π2x dx1−cos⁡2tsin⁡2xf(t) = \int_0^{\pi} \frac{2x\,dx}{1-\cos^2 t \sin^2 x}, 0<t<π0 < t < \pi, then the value of…HardNumerical value
  6. 1 Feb 2024, Shift 1 · Q10The value of the intergral ∫0π/4x dxsin⁡4(2x)+cos⁡4(2x)\int_0^{\pi/4}\frac{x\,dx}{\sin^4(2x)+\cos^4(2x)} equals :HardSingle correct
  7. 1 Feb 2024, Shift 2 · Q11The value of ∫−01(2x3−3x2−x+1)13 dx\int_{-0}^{1}(2x^3-3x^2-x+1)^{\frac{1}{3}}\,dx is equal to :MediumSingle correct
  8. 27 Jan 2024, Shift 1 · Q12If (a,b)(a, b) be the orthocentre of the triangle whose vertices are (1,2)(1, 2), (2,3)(2, 3) and (3,1)(3, 1), and I1=∫abxsin⁡(4x−x2) dxI_1=\int_a^b x\sin(4x-x^2)\,dx,…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.