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 idea in other shifts

Asked 4× in all

24 Feb 2021, Shift 1 · Q67The function $f(x) = \frac{4x^3 - 3x^2}{6} - 2\sin x + (2x - 1)\cos x$ :MediumSingle 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.