JEE Main Maths · Continuity and Differentiability

Continuity and Differentiability in JEE Main

Name: Continuity and Differentiability: JEE Main previous year questions
Creator: Lumi

Continuity and Differentiability (Maths, Continuity and Differentiability) came 33 times in 28 of the 42 JEE Main shifts Lumi analysed, across 14 distinct ideas. 17 of them came in 2024–26; it was last asked in 2026.

Questions: 33; in 28 shifts
Ideas asked: 14; 11 asked more than once
Numerical answer: 12; 36% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 20Hard 12

Format

Single correct20 Q
Numerical value12 Q
Two statements1 Q

Ideas inside the topic

14 ideas

Continuity involving GIF and Fractional Part7 Q
Continuity and Differentiability of Composite Functions3 Q
Differentiability via Functional Equations3 Q
Finding Unknowns using Differentiability3 Q
Differentiability of Max/Min Functions2 Q
Differentiability of Modulus Functions2 Q
Piecewise Differentiability2 Q
Continuity at a Point2 Q
Modulus Traps in Trigonometric Functions2 Q
Finding Unknown Constants for Continuity2 Q
Finding Unknowns using Continuity2 Q
Continuity and Differentiability of Integral Functions1 Q

Where it sits

Part of Continuity and Differentiability, which had 48 questions in all. Continuity and Differentiability accounts for 69% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Every question

All 33 Continuity and Differentiability 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
4 Apr 2026, Shift 1 · Q25The number of points, at which the function $f(x)=\max\{6x,\ 2+3x^2\}+|x-1|\cos\left|x^2-\frac14\right|$ , $x\in(-\pi,\pi)$ , is not…HardNumerical value
4 Apr 2026, Shift 2 · Q22Let $f(x)=\begin{cases}e^{x-1}, & x<0\\ x^2-5x+6, & x\ge0\end{cases}$ and $g(x)=f(|x|)+|f(x)|$ . If the number of points where $g$ is not…MediumNumerical value
5 Apr 2026, Shift 1 · Q19Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3}$ for all…MediumSingle correct
6 Apr 2026, Shift 2 · Q25Let $f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases}$ and $g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}$ …HardNumerical value
8 Apr 2026, Shift 2 · Q13For the function $f(x) = \mathrm{e}^{\sin|x|} - |x|$ , $x \in \mathbf{R}$ , consider the following statements : Statement I : $f$ is…MediumTwo statements
8 Apr 2026, Shift 2 · Q19Let $f(x) = \begin{cases} \frac{1}{3}, & x \le \pi/2 \\ \frac{b(1 - \sin x)}{(\pi - 2x)^2}, & x > \pi/2 \end{cases}$ . If $f$ is continuous…MediumSingle correct
2 Apr 2025, Shift 1 · Q14Let $f:\mathbf{R}\to\mathbf{R}$ be a twice differentiable function such that…HardSingle correct
3 Apr 2025, Shift 1 · Q17Let $f(x) = \begin{cases} (1+ax)^{1/x}, & x < 0 \\ 1+b, & x = 0 \\ \dfrac{(x+4)^{1/2} - 2}{(x+c)^{1/3} - 2}, & x > 0 \end{cases}$ be…MediumSingle correct
7 Apr 2025, Shift 2 · Q25If the function $f(x)=\frac{\tan(\tan x)-\sin(\sin x)}{\tan x-\sin x}$ is continuous at $x=0$ , then $f(0)$ is equal to ________.HardNumerical value
6 Apr 2024, Shift 2 · Q10Suppose for a differentiable function $h$ , $h(0)=0$ , $h(1)=1$ and $h'(0)=h'(1)=2$ . If $g(x)=h(e^x)e^{h(x)}$ , then $g'(0)$ is equal to :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
9 Apr 2024, Shift 1 · Q24Let $f:(0,\pi)\to\mathbf{R}$ be a function given by…HardNumerical value
30 Jan 2024, Shift 2 · Q7Let $f: \mathbb{R} - \{0\} \to \mathbb{R}$ be a function satisfying $f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)}$ for all…MediumSingle correct
30 Jan 2024, Shift 2 · Q8Let $a$ and $b$ be real constants such that the function $f$ defined by…MediumSingle correct
31 Jan 2024, Shift 1 · Q9Let $g(x)$ be a linear funchion and $f(x)=\begin{cases}g(x), & x\leq0\\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}}, & x>0\end{cases}$ is…HardSingle correct
31 Jan 2024, Shift 2 · Q8Consider the function $f:(0,\infty)\to\mathbb{R}$ defined by $f(x)=e^{-|\log_e x|}$ . If $m$ and $n$ be respectively the number of points…MediumSingle 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
8 Apr 2023, Shift 2 · Q25Let $k$ and $m$ be positive real numbers such that the function…MediumNumerical 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
25 Jul 2022, Shift 1 · Q26Let $f(x)=\begin{cases}\left|\,4x^2-8x+5\,\right|, & \text{if } 8x^2-6x+1\ge0\\ [\,4x^2-8x+5\,], & \text{if } 8x^2-6x+1<0,\end{cases}$ …HardNumerical value
24 Jun 2022, Shift 1 · Q25The number of points where the function…HardNumerical value
29 Jun 2022, Shift 1 · Q4Let $f: \mathbf{R} \to \mathbf{R}$ be a function defined by :…HardSingle correct
3 Aug 2021, Shift 2 · Q69If for non-zero distinct real numbers $a$ , $b$ and $c$ ,…MediumSingle correct
25 Jul 2021, Shift 1 · Q64Let $f:[0,\infty)\to[0,\infty)$ be defined as $f(x)=\int_0^x[y]\,dy$ where $[x]$ is the greatest integer less than or equal to $x$ . Which…MediumSingle correct
25 Jul 2021, Shift 1 · Q65Let $f:\mathbf{R}\to\mathbf{R}$ be defined as…MediumSingle correct
16 Mar 2021, Shift 2 · Q69Let $\alpha\in\mathbf R$ be such that the function…HardSingle correct
16 Mar 2021, Shift 2 · Q85Let $f:\mathbf R\to\mathbf R$ and $g:\mathbf R\to\mathbf R$ be defined as $f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases}$ and…MediumNumerical value
18 Mar 2021, Shift 1 · Q70If $f(x)=\begin{cases}\dfrac{1}{|x|} & ;\ |x|\ge1\\ ax^2+b & ;\ |x|<1\end{cases}$ is differentiable at every point of the domain, then the…MediumSingle correct
8 Jan 2020, Shift 1 · Q58Let $f(x)=x\cos^{-1}(-\sin|x|)$ , $x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ , then which of the following is true ?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
2 Sep 2020, Shift 1 · Q59If a function $f(x)$ defined by…MediumSingle correct
6 Sep 2020, Shift 2 · Q58Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined by $f(x)=\max\{x,x^2\}$ . Let S denote the set of all points in $\mathbf{R}$ , where…EasySingle correct