JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

f:\mathbf{R}\to\mathbf{R}

and

g:\mathbf{R}\to\mathbf{R}

be two functions defined by

f(x)=\log_e(x^2+1)-e^{-x}+1

and

g(x)=\frac{1-2e^{2x}}{e^x}

. Then, for which of the following range of

\alpha

, the inequality

f\left(g\left(\frac{(\alpha-1)^2}{3}\right)\right)>f\left(g\left(\alpha-\frac{5}{3}\right)\right)

holds ?

(1) $(2, 3)$ Official answer
(2) $(-2, -1)$
(3) $(1, 2)$
(4) $(-1, 1)$

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Monotonicity of Composite Functions

Same topic in other shifts

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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.