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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 July 2022, Shift 2, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

If the maximum value of aa, for which the function fa(x)=tan⁡−12x−3ax+7f_a(x)=\tan^{-1}2x-3ax+7 is non-decreasing in (−π6,π6)\left(-\frac{\pi}{6},\frac{\pi}{6}\right), is aˉ\bar{a}, then faˉ(π8)f_{\bar{a}}\left(\frac{\pi}{8}\right) is equal to
  1. (1)8−9π4(9+π2)8-\frac{9\pi}{4(9+\pi^2)}
  2. (2)8−4π9(4+π2)8-\frac{4\pi}{9(4+\pi^2)}
  3. (3)8(1+π29+π2)8\left(\frac{1+\pi^2}{9+\pi^2}\right)
  4. (4)8−π48-\frac{\pi}{4}

Official answer

Dropped by NTA (marks given to all)

NTA final key.

Chapter
Application of Derivatives
Topic
Monotonicity
Idea tested
No close match in our taxonomy

Same topic in other shifts

All Monotonicity questions
  1. 8 Apr 2025, Shift 2 · Q17Let the function f(x)=x3+3x+3f(x) = \frac{x}{3} + \frac{3}{x} + 3, x≠0x \neq 0 be strictly increasing in…EasySingle correct
  2. 5 Apr 2024, Shift 1 · Q5For the function f(x)=sin⁡x+3x−2π(x2+x)f(x)=\sin x+3x-\frac{2}{\pi}(x^2+x), where x∈[0,π2]x\in\left[0,\frac{\pi}{2}\right], consider the following two statements :…MediumTwo statements
  3. 6 Apr 2024, Shift 1 · Q9The interval in which the function f(x)=xxf(x)=x^x, x>0x>0, is strictly increasing isEasySingle correct
  4. 8 Apr 2024, Shift 1 · Q7For the function f(x)=(cos⁡x)−x+1f(x)=(\cos x)-x+1, x∈Rx\in\mathbb{R}, between the following two statements (S1) f(x)=0f(x)=0 for only one value of xx in…MediumTwo statements
  5. 1 Feb 2024, Shift 1 · Q7If 5f(x)+4f(1x)=x2−2, ∀ x≠05f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0 and y=9x2f(x)y=9x^2f(x), then yy is strictly increasing in :HardSingle correct
  6. 10 Apr 2023, Shift 2 · Q9Let g(x)=f(x)+f(1−x)g(x) = f(x) + f(1-x) and f′′(x)>0, x∈(0,1)f''(x) > 0,\ x \in (0,1). If gg is decreasing in the interval (0,α)(0, \alpha) and increasing in the…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.