JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

Let

g:(0,\infty)\to\mathbf{R}

be a differentiable function such that

\int\left(\frac{x(\cos x-\sin x)}{e^x+1}+\frac{g(x)\left(e^x+1-xe^x\right)}{(e^x+1)^2}\right)\mathrm{d}x=\frac{x\,g(x)}{e^x+1}+c

, for all

x>0

, where c is an arbitrary constant. Then :

(1) $g$ is decreasing in $\left(0,\frac{\pi}{4}\right)$
(2) $g'$ is increasing in $\left(0,\frac{\pi}{4}\right)$
(3) $g+g'$ is increasing in $\left(0,\frac{\pi}{2}\right)$
(4) $g-g'$ is increasing in $\left(0,\frac{\pi}{2}\right)$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Trigonometric Monotonicity by Quadrant

Same topic in other shifts

All Monotonicity questions

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.