Learn

Friday, 9 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 25 July 2021, Shift 1, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

Let f(x)=3sin⁡4x+10sin⁡3x+6sin⁡2x−3f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3, x∈[−π6,π2]x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]. Then, ff is :
  1. (1)increasing in (−π6,0)\left(-\frac{\pi}{6},0\right)
  2. (2)decreasing in (0,π2)\left(0,\frac{\pi}{2}\right)
  3. (3)increasing in (−π6,π2)\left(-\frac{\pi}{6},\frac{\pi}{2}\right)
  4. (4)decreasing in (−π6,0)\left(-\frac{\pi}{6},0\right)Official answer

Official answer

Option 4

NTA final key.

Chapter
Application of Derivatives
Topic
Monotonicity
Idea tested
Finding Intervals

Same idea in other shifts

Asked 3× in all
  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. 16 Mar 2021, Shift 2 · Q64Let ff be a real valued function, defined on R−{−1,1}\mathbf R-\{-1,1\} and given by f(x)=3log⁡e∣x−1x+1∣−2x−1f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}.…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 42 of the 174 JEE Main shifts held from 2017 to 2026.