JEE Main 2024 · MathsMultiple choiceTwo statementsMediumApplication

JEE Main 5 April 2024, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

For the function

f(x)=\sin x+3x-\frac{2}{\pi}(x^2+x)

, where

x\in\left[0,\frac{\pi}{2}\right]

, consider the following two statements : (I)

f

is increasing in

\left(0,\frac{\pi}{2}\right)

. (II)

f'

is decreasing in

\left(0,\frac{\pi}{2}\right)

. Between the above two statements,

(1)only (I) is true.
(2)only (II) is true.
(3)neither (I) nor (II) is true.
(4)both (I) and (II) are true.Official answer

Official answer

Option 4

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Monotonicity of the Derivative Function

Same topic in other shifts

All Monotonicity questions

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6 Apr 2024, Shift 1 · Q9The interval in which the function $f(x)=x^x$ , $x>0$ , is strictly increasing isEasySingle correct
8 Apr 2024, Shift 1 · Q7For the function $f(x)=(\cos x)-x+1$ , $x\in\mathbb{R}$ , between the following two statements (S1) $f(x)=0$ for only one value of $x$ in…MediumTwo statements
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
10 Apr 2023, Shift 2 · Q9Let $g(x) = f(x) + f(1-x)$ and $f''(x) > 0,\ x \in (0,1)$ . If $g$ is decreasing in the interval $(0, \alpha)$ and increasing in the…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.