JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q10

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

For the function

f(x)=4\log_e(x-1)-2x^2+4x+5,\ x>1

, which one of the following is NOT correct ?

(1) $f$ is increasing in $(1, 2)$ and decreasing in $(2, \infty)$
(2) $f(x)=-1$ has exactly two solutions
(3) $f'(e)-f''(2)<0$ Official answer
(4) $f(x)=0$ has a root in the interval $(e, e+1)$

Official answer

Option 3

NTA final key (2022 Session 1).

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

Same topic in other shifts

All Monotonicity questions

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11 Apr 2023, Shift 1 · Q10Let $f : [2, 4] \to \mathbb{R}$ be a differentiable function such that $(x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]$ …HardTwo statements
25 Jul 2021, Shift 1 · Q67Let $f(x)=3\sin^4x+10\sin^3x+6\sin^2x-3$ , $x\in\left[-\frac{\pi}{6},\frac{\pi}{2}\right]$ . Then, $f$ is :MediumSingle correct
16 Mar 2021, Shift 2 · Q64Let $f$ be a real valued function, defined on $\mathbf R-\{-1,1\}$ and given by $f(x)=3\log_e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}$ .…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.