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Friday, 9 October

JEE Main Maths · Class 12

Continuity and Differentiability: JEE Main previous year questions

Continuity and Differentiability had 48 questions in the 42 JEE Main shifts Lumi analysed, about 1.1 a shift, asked in 36 of 42 shifts. It ranks 12 of 22 Maths chapters by questions; 38% of its questions were hard.

Questions
48
in 36 of 42 shifts
A shift, on average
1.1
of 25 Maths questions
Since 2024
-0.2
1.1 a shift in 2017–23, 1.0 in 2024–26
Numerical answer
14
29% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
06121’177’206’214’224’2310’245’2511’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20207
  • 20216
  • 20224
  • 20234
  • 202410
  • 20255
  • 202611
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

7 topics and 25 distinct ideas; 12 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

3 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
12 repeat

Study it on Lumi

Continuity and Differentiability: the interactive lesson

Every question

All 48 Continuity and Differentiability questions

Newest first. Each opens with its options and the official answer.

2026 11 questions

  1. 2 Apr 2026, Shift 1 · Q16If lim⁡x→2sin⁡(x3−5x2+ax+b)(x−1−1)log⁡e(x−1)=m\lim_{x\to2}\frac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)}=m, then a+b+ma+b+m is equal to :HardSingle correct
  2. 2 Apr 2026, Shift 2 · Q25The number of points in the interval [2,4][2, 4], at which the function f(x)=x2−x−1⌊x⌋−12f(x) = x^2 - x - \frac{1}{\lfloor x \rfloor - \frac{1}{2}}, where…MediumNumerical value
  3. 4 Apr 2026, Shift 1 · Q16If y=tan⁡−1(3cos⁡x−4sin⁡x4cos⁡x+3sin⁡x)+2tan⁡−1(x1+1−x2)y=\tan^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2\tan^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right), then dydx\frac{dy}{dx}…MediumSingle correct
  4. 4 Apr 2026, Shift 1 · Q17Let ff be a real polynomial of degree nn such that f(x)=f′(x)f′′(x)f(x)=f'(x)f''(x), for all x∈Rx\in\mathbb{R}. If f(0)=0f(0)=0, then…HardSingle correct
  5. 4 Apr 2026, Shift 1 · Q25The number of points, at which the function f(x)=max⁡{6x, 2+3x2}+∣x−1∣cos⁡∣x2−14∣f(x)=\max\{6x,\ 2+3x^2\}+|x-1|\cos\left|x^2-\frac14\right|, x∈(−π,π)x\in(-\pi,\pi), is not…HardNumerical value
  6. 4 Apr 2026, Shift 2 · Q22Let f(x)={ex−1,x<0x2−5x+6,x≥0f(x)=\begin{cases}e^{x-1}, & x<0\\ x^2-5x+6, & x\ge0\end{cases} and g(x)=f(∣x∣)+∣f(x)∣g(x)=f(|x|)+|f(x)|. If the number of points where gg is not…MediumNumerical value
  7. 5 Apr 2026, Shift 1 · Q19Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a differentiable function such that f(x+y3)=f(x)+f(y)3f\left(\frac{x+y}{3}\right) = \frac{f(x)+f(y)}{3} for all…MediumSingle correct
  8. 5 Apr 2026, Shift 2 · Q20Let f(x)f(x) and g(x)g(x) be twice differentiable functions satisfying f′′(x)=g′′(x)f''(x)=g''(x) for all x∈Rx \in \mathbf{R}, f′(1)=2g′(1)=4f'(1)=2g'(1)=4 and…MediumSingle correct
  9. 6 Apr 2026, Shift 2 · Q25Let f(x)={x3+8;x<0,x2−4;x≥0,f(x)=\begin{cases}x^3+8;&x<0,\\x^2-4;&x\ge0,\end{cases} and g(x)={(x−8)1/3;x<0,(x+4)1/2;x≥0.g(x)=\begin{cases}(x-8)^{1/3};&x<0,\\(x+4)^{1/2};&x\ge0.\end{cases}…HardNumerical value
  10. 8 Apr 2026, Shift 2 · Q13For the function f(x)=esin⁡∣x∣−∣x∣f(x) = \mathrm{e}^{\sin|x|} - |x|, x∈Rx \in \mathbf{R}, consider the following statements : Statement I : ff is…MediumTwo statements
  11. 8 Apr 2026, Shift 2 · Q19Let f(x)={13,x≤π/2b(1−sin⁡x)(π−2x)2,x>π/2f(x) = \begin{cases} \frac{1}{3}, & x \le \pi/2 \\ \frac{b(1 - \sin x)}{(\pi - 2x)^2}, & x > \pi/2 \end{cases}. If ff is continuous…MediumSingle correct

2025 5 questions

  1. 2 Apr 2025, Shift 1 · Q14Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a twice differentiable function such that…HardSingle correct
  2. 3 Apr 2025, Shift 1 · Q17Let f(x)={(1+ax)1/x,x<01+b,x=0(x+4)1/2−2(x+c)1/3−2,x>0f(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
  3. 4 Apr 2025, Shift 2 · Q16Let ff be a differentiable function on R\mathbf{R} such that f(2)=1f(2)=1, f′(2)=4f'(2)=4. Let…HardSingle correct
  4. 7 Apr 2025, Shift 1 · Q25The number of points of discontinuity of the function f(x)=[x22]−[x]f(x) = \left[\frac{x^2}{2}\right] - [\sqrt{x}], x∈[0,4]x \in [0, 4], where [⋅][\cdot]…MediumNumerical value
  5. 7 Apr 2025, Shift 2 · Q25If the function f(x)=tan⁡(tan⁡x)−sin⁡(sin⁡x)tan⁡x−sin⁡xf(x)=\frac{\tan(\tan x)-\sin(\sin x)}{\tan x-\sin x} is continuous at x=0x=0, then f(0)f(0) is equal to ________.HardNumerical value

2024 10 questions

  1. 6 Apr 2024, Shift 2 · Q10Suppose for a differentiable function hh, h(0)=0h(0)=0, h(1)=1h(1)=1 and h′(0)=h′(1)=2h'(0)=h'(1)=2. If g(x)=h(ex)eh(x)g(x)=h(e^x)e^{h(x)}, then g′(0)g'(0) is equal to :MediumSingle correct
  2. 6 Apr 2024, Shift 2 · Q24Let [t][t] denote the greatest integer less than or equal to tt. Let f:[0,∞)→Rf:[0,\infty)\to\mathbb{R} be a function defined by…MediumNumerical value
  3. 9 Apr 2024, Shift 1 · Q24Let f:(0,π)→Rf:(0,\pi)\to\mathbf{R} be a function given by…HardNumerical value
  4. 9 Apr 2024, Shift 2 · Q8If log⁡ey=3sin⁡−1x\log_e y=3\sin^{-1}x, then (1−x2)y′′−xy′(1-x^2)y''-xy' at x=12x=\frac{1}{2} is equal toMediumSingle correct
  5. 29 Jan 2024, Shift 1 · Q9Suppose f(x)=(2x+2−x)tan⁡xtan⁡−1(x2−x+1)(7x2+3x+1)3f(x)=\frac{(2^x+2^{-x})\tan x\sqrt{\tan^{-1}(x^2-x+1)}}{(7x^2+3x+1)^3}. Then the value of f′(0)f'(0) is equal toHardSingle correct
  6. 30 Jan 2024, Shift 2 · Q7Let f:R−{0}→Rf: \mathbb{R} - \{0\} \to \mathbb{R} be a function satisfying f(xy)=f(x)f(y)f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)} for all…MediumSingle correct
  7. 30 Jan 2024, Shift 2 · Q8Let aa and bb be real constants such that the function ff defined by…MediumSingle correct
  8. 31 Jan 2024, Shift 1 · Q9Let g(x)g(x) be a linear funchion and f(x)={g(x),x≤0(1+x2+x)1x,x>0f(x)=\begin{cases}g(x), & x\leq0\\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}}, & x>0\end{cases} is…HardSingle correct
  9. 31 Jan 2024, Shift 2 · Q8Consider the function f:(0,∞)→Rf:(0,\infty)\to\mathbb{R} defined by f(x)=e−∣log⁡ex∣f(x)=e^{-|\log_e x|}. If mm and nn be respectively the number of points…MediumSingle correct
  10. 31 Jan 2024, Shift 2 · Q9Let f:R→(0,∞)f:\mathbb{R}\to(0,\infty) be strictly increasing function such that lim⁡x→∞f(7x)f(x)=1\lim_{x\to\infty}\frac{f(7x)}{f(x)}=1. Then, the value of…HardSingle correct

2023 4 questions

  1. 6 Apr 2023, Shift 1 · Q9If 2xy+3yx=202x^y+3y^x=20, then dydx\frac{dy}{dx} at (2,2)(2,2) is equal to:MediumSingle correct
  2. 6 Apr 2023, Shift 1 · Q25Let a∈Za\in\mathbb{Z} and [t][t] be the greatest integer ≤t\le t. Then the number of points, where the function f(x)=[a+13sin⁡x]f(x)=[a+13\sin x],…HardNumerical value
  3. 8 Apr 2023, Shift 2 · Q25Let kk and mm be positive real numbers such that the function…MediumNumerical value
  4. 11 Apr 2023, Shift 1 · Q7Let f(x)=[x2−x]+∣−x+[x]∣f(x) = [x^2 - x] + |-x + [x]|, where x∈Rx \in \mathbb{R} and [t][t] denotes the greatest integer less than or equal to tt. Then, ff isMediumSingle correct

2022 4 questions

  1. 25 Jul 2022, Shift 1 · Q26Let f(x)={∣ 4x2−8x+5 ∣,if 8x2−6x+1≥0[ 4x2−8x+5 ],if 8x2−6x+1<0,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
  2. 28 Jul 2022, Shift 1 · Q29lim⁡x→0((x+2cos⁡x)3+2(x+2cos⁡x)2+3sin⁡(x+2cos⁡x)(x+2)3+2(x+2)2+3sin⁡(x+2))100x\lim_{x\to0}\left(\frac{(x+2\cos x)^3+2(x+2\cos x)^2+3\sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} is equal to…HardNumerical value
  3. 24 Jun 2022, Shift 1 · Q25The number of points where the function…HardNumerical value
  4. 29 Jun 2022, Shift 1 · Q4Let f:R→Rf: \mathbf{R} \to \mathbf{R} be a function defined by :…HardSingle correct

2021 6 questions

  1. 3 Aug 2021, Shift 2 · Q69If for non-zero distinct real numbers aa, bb and cc,…MediumSingle correct
  2. 25 Jul 2021, Shift 1 · Q64Let f:[0,∞)→[0,∞)f:[0,\infty)\to[0,\infty) be defined as f(x)=∫0x[y] dyf(x)=\int_0^x[y]\,dy where [x][x] is the greatest integer less than or equal to xx. Which…MediumSingle correct
  3. 25 Jul 2021, Shift 1 · Q65Let f:R→Rf:\mathbf{R}\to\mathbf{R} be defined as…MediumSingle correct
  4. 16 Mar 2021, Shift 2 · Q69Let α∈R\alpha\in\mathbf R be such that the function…HardSingle correct
  5. 16 Mar 2021, Shift 2 · Q85Let f:R→Rf:\mathbf R\to\mathbf R and g:R→Rg:\mathbf R\to\mathbf R be defined as f(x)={x+a,x<0∣x−1∣,x≥0f(x)=\begin{cases}x+a, & x<0\\ |x-1|, & x\ge0\end{cases} and…MediumNumerical value
  6. 18 Mar 2021, Shift 1 · Q70If f(x)={1∣x∣; ∣x∣≥1ax2+b; ∣x∣<1f(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

2020 7 questions

  1. 8 Jan 2020, Shift 1 · Q58Let f(x)=xcos⁡−1(−sin⁡∣x∣)f(x)=x\cos^{-1}(-\sin|x|), x∈[−π2,π2]x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right], then which of the following is true ?HardSingle correct
  2. 8 Jan 2020, Shift 1 · Q59If c is a point at which Rolle's theorem holds for the function, f(x)=log⁡e(x2+α7x)f(x)=\log_e\left(\dfrac{x^2+\alpha}{7x}\right) in the interval [3,4][3,4],…MediumSingle correct
  3. 9 Jan 2020, Shift 2 · Q58Let [t][t] denote the greatest integer ≤t\le t and lim⁡x→0x[4x]=A\lim_{x\to0}x\left[\frac{4}{x}\right]=A. Then the function, f(x)=[x2]sin⁡(πx)f(x)=[x^2]\sin(\pi x) is…MediumSingle correct
  4. 9 Jan 2020, Shift 2 · Q60Let ff and gg be differentiable functions on R\mathbf{R} such that f∘gf\circ g is the identity function. If for some a,b∈Ra,b\in\mathbf{R},…EasySingle correct
  5. 2 Sep 2020, Shift 1 · Q59If a function f(x)f(x) defined by…MediumSingle correct
  6. 6 Sep 2020, Shift 2 · Q57For all twice differentiable functions f:R→Rf:\mathbf{R}\to\mathbf{R}, with f(0)=f(1)=f′(0)=0f(0)=f(1)=f'(0)=0,MediumSingle correct
  7. 6 Sep 2020, Shift 2 · Q58Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a function defined by f(x)=max⁡{x,x2}f(x)=\max\{x,x^2\}. Let S denote the set of all points in R\mathbf{R}, where…EasySingle correct

2017 1 questions

  1. 2 Apr 2017 (offline) · Q71If for x∈(0,14)x\in\left(0,\frac{1}{4}\right), the derivative of tan⁡−1(6xx1−9x3)\tan^{-1}\left(\frac{6x\sqrt{x}}{1-9x^3}\right) is x⋅g(x)\sqrt{x}\cdot g(x), then…MediumSingle correct

Pattern: Asked most years.