JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

g(x) = f(x) + f(1-x)

and

f''(x) > 0,\ x \in (0,1)

. If

g

is decreasing in the interval

(0, \alpha)

and increasing in the interval

(\alpha, 1)

, then

\tan^{-1}(2\alpha) + \tan^{-1}\left(\frac{1}{\alpha}\right) + \tan^{-1}\left(\frac{\alpha+1}{\alpha}\right)

is equal to

(1) $\frac{5\pi}{4}$
(2) $\frac{3\pi}{2}$
(3) $\frac{3\pi}{4}$
(4) $\pi$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Strict Monotonicity

Same topic in other shifts

All Monotonicity questions

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1 Feb 2024, Shift 1 · Q7If $5f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0$ and $y=9x^2f(x)$ , then $y$ is strictly increasing in :HardSingle correct
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

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.