JEE Main Maths · Continuity and Differentiability

Continuity involving GIF and Fractional Part

Continuity involving GIF and Fractional Part (Continuity and Differentiability) was asked 7 times in 7 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 4 of the 7 had a numerical answer.

Times asked: 7; in 7 shifts
Years: 2020–2026
Usual format: Numerical value; Multi-step
Pattern: Asked most years; repeats across shifts

How it is asked

Count discontinuities of greatest integer function
Continuity with fractional part function

Difficulty

Easy 0Medium 4Hard 3

Where it sits

Chapter: Continuity and Differentiability. Topic: Continuity and Differentiability, 33 questions over 14 ideas.

All 7 questions

Newest first, each with its options and official answer.

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
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