JEE Main 2026 · MathsNumerical answerNumerical valueMediumApplication

JEE Main 2 April 2026, Shift 2, Maths Q25

Question 25 of 75 in this shift, Maths question 25 of 25, Section B.

The 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

[\cdot]

denotes the greatest integer function, is discontinuous, is

Official answer

NTA final key.

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

Same idea in other shifts

Asked 7× in all

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
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
24 Jun 2022, Shift 1 · Q25The number of points where the function…HardNumerical value
16 Mar 2021, Shift 2 · Q69Let $\alpha\in\mathbf R$ be such that the function…HardSingle correct
9 Jan 2020, Shift 2 · Q58Let $[t]$ denote the greatest integer $\le t$ and $\lim_{x\to0}x\left[\frac{4}{x}\right]=A$ . Then the function, $f(x)=[x^2]\sin(\pi x)$ is…MediumSingle correct

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.