JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q67

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

The function

f(x) = \frac{4x^3 - 3x^2}{6} - 2\sin x + (2x - 1)\cos x

(1)increases in $\left[\frac{1}{2}, \infty\right)$ Official answer
(2)decreases in $\left[\frac{1}{2}, \infty\right)$
(3)increases in $\left(-\infty, \frac{1}{2}\right]$
(4)decreases in $\left(-\infty, \frac{1}{2}\right]$

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: First Derivative Test

Same idea in other shifts

Asked 4× in all

24 Jun 2022, Shift 1 · Q10For the function $f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1$ , which one of the following is NOT correct ?HardSingle correct
17 Mar 2021, Shift 2 · Q69Consider the function $f:\mathbf{R}\to\mathbf{R}$ defined by…HardSingle correct
2 Sep 2020, Shift 2 · Q61Let $f:(-1,\infty)\to\mathbf{R}$ be defined by $f(0)=1$ and $f(x)=\frac{1}{x}\log_e(1+x)$ , $x\neq 0$ . Then the function $f$ :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.