For 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 $[0,\pi]$. (S2) $f(x)$ is decreasing in $\left[0,\frac{\pi}{2}\right]$ and increasing in $\left[\frac{\pi}{2},\pi\right]$.

Option 2: Only (S1) is correct.

Both (S1) and (S2) are correct.

Both (S1) and (S2) are incorrect.

JEE Main 2024 · MathsMultiple choiceTwo statementsMediumApplication

JEE Main 8 April 2024, Shift 1, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

For 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

[0,\pi]

. (S2)

f(x)

is decreasing in

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

and increasing in

\left[\frac{\pi}{2},\pi\right]

(1)Both (S1) and (S2) are correct.
(2)Only (S1) is correct.Official answer
(3)Only (S2) is correct.
(4)Both (S1) and (S2) are incorrect.

Official answer

Option 2

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Counting Roots using Monotonicity

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.