JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

The number of points where the function

f(x)=\begin{cases}|2x^2-3x-7| & \text{if } x\le -1\\ [4x^2-1] & \text{if } -1<x<1\\ |x+1|+|x-2| & \text{if } x\ge 1,\end{cases}

[t]

denotes the greatest integer

\le t

, is discontinuous is ______.

Official answer

NTA final key (2022 Session 1).

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity involving GIF and Fractional Part

Same idea in other shifts

Asked 17× in all

2 Apr 2026, Shift 2 · Q25The number of points in the interval $[2, 4]$ , at which the function $f(x) = x^2 - x - \frac{1}{\lfloor x \rfloor - \frac{1}{2}}$ , where…MediumNumerical value
5 Apr 2024, Shift 2 · Q10Let $f : [-1, 2] \to \mathbf{R}$ be given by $f(x) = 2x^2 + x + [x^2] - [x]$ , where $[t]$ denotes the greatest integer less than or equal…MediumSingle correct
6 Apr 2024, Shift 2 · Q24Let $[t]$ denote the greatest integer less than or equal to $t$ . Let $f:[0,\infty)\to\mathbb{R}$ be a function defined by…MediumNumerical value
27 Jan 2024, Shift 1 · Q8Consider the function.…HardSingle correct
6 Apr 2023, Shift 1 · Q25Let $a\in\mathbb{Z}$ and $[t]$ be the greatest integer $\le t$ . Then the number of points, where the function $f(x)=[a+13\sin x]$ ,…HardNumerical value
11 Apr 2023, Shift 1 · Q7Let $f(x) = [x^2 - x] + |-x + [x]|$ , where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$ . Then, $f$ isMediumSingle correct
12 Apr 2023, Shift 1 · Q25Let $[x]$ be the greatest integer $\le x$ . Then the number of points in the interval $(-2,1)$ , where the function…MediumNumerical value
29 Jul 2022, Shift 2 · Q26If $[t]$ denotes the greatest integer $\leq t$ , then the number of points, at which the function…HardNumerical value

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.