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Sunday, 25 October

JEE Main · Maths · Class 12

Continuity and Differentiability: JEE Main previous year questions

134 questions in 94 of the 108 JEE Main shifts Lumi analysed, asked in 8 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
134
in 94 of 108 shifts · 8 of 8 years
Average a shift
1.1
of 25 Maths · 1.0 since 2024 0.0
Typical range
0.7–1.2
questions a shift; fewest 0.6, most 1.6
Weighted estimate
1.0
model, recent years count more · about 4.2 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Continuity and Differentiability

Priority

Should do

One of the 6 Maths chapters that took Maths from half to 80% of its questions in the 108 shifts analysed. How bands are set

Past questions
134in 94 of 108 shifts
Study plan gives it
19 hover 12 months; 14 h over 6
Study this chapter →

Ideas asked most often

  1. Continuity involving GIF and Fractional Part17×
  2. Differentiability via Functional Equations10×
  3. Finding Unknown Constants for Continuity10×
  4. Differentiability of Modulus Functions9×
  5. Continuity at a Point8×

127 of the 183 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 14% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Continuity and Differentiability at a glance

  1. 01

    86%

    of its 37 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    69%

    of the 183 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    31%

    of its questions asked for a numerical answer, 1.1 times the Maths average.

  4. 04

    40%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240.9’171.6’201.1’211.1’220.7’231.2’240.6’251.2’26

Raw count: 2017: 1 in 1 shift · 2020: 19 in 12 shifts · 2021: 31 in 24 shifts · 2022: 31 in 24 shifts · 2023: 10 in 12 shifts · 2024: 26 in 18 shifts · 2025: 5 in 8 shifts · 2026: 11 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step40%
  • Numerical answer31%
  • Calculation12%
  • Application10%
  • Conceptual5%
  • Two statements2%
  • Recall, single correct1%

Most common asks: unknown constants from continuity of piecewise function (13); count discontinuities of greatest integer function (10); count non-differentiable points of modulus function (6).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#36
of 70 by weighted estimate
Rank in Maths
#13
of 21 chapters
Share of Maths
4.2%
of its questions, all shifts analysed
Busiest year
2020
1.6 questions a shift
Year to year
Some swing
varies by about 0.3 questions a shift
Long-run direction
-0.01
questions a shift, per year
Easy questions
6%
40% rated hard
Numerical answer
31%
1.1× the Maths rate
With a figure
1%
graph, diagram or structure
Study time
19 h
14 h on a 6-month plan
Marks per study hour
0.22
#54 of 70 chapters
Foundation for others
47%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20171
  • 202019
  • 202131
  • 202231
  • 202310
  • 202426
  • 20255
  • 202611
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step63%
  • Calculation17%
  • Application13%
  • Conceptual4%
  • Data or graph1%
  • Recall1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 183 ideas. In the 108 shifts analysed, JEE Main built a question around 38 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
38
Touched on in a question
18
Never asked
127

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 6 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
026+questions in that year’s analysed shifts, shaded per shift
  • Continuity and Differentiability

    As a topic: 94 questions in 7 of 8 years, most often single correct, 31% numerical answer. Recent asks: statement I/II on differentiability and monotonicity; find constant from continuity then integral; count discontinuities of composite piecewise function.

  • Chain Rule

    As a topic: 31 questions in 6 of 8 years, most often single correct, 26% numerical answer.

  • Mean Value Theorem

    As a topic: 7 questions in 3 of 8 years, most often single correct.

  • Inverse Trig Identities

    As a topic: 51 questions in 8 of 8 years, most often single correct, 22% numerical answer.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open92 · 69%10262271737

    18 ideas inside

    • OpenRepeated15 · 16%22433
    • OpenRepeated10 · 11%232
    • OpenRepeated10 · 11%433
    • OpenRepeated9 · 10%322
    • OpenRepeated8 · 9%2222
    • OpenRepeated7 · 8%3
    • OpenRepeated7 · 8%23
    • OpenRepeated6 · 7%2
    • OpenRepeated4 · 4%2
    • OpenRepeated3 · 3%
    • OpenRepeated3 · 3%
    • OpenRepeated3 · 3%
    • OpenRepeated2 · 2%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open21 · 16%43635
  • Open4 · 3%3
  • Open3 · 2%
  • Open3 · 2%
  • Open2 · 1%
  • Open2 · 1%
  • Open1 · 1%

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 39 different ideas were tested; 20 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 134 Continuity and Differentiability questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 202611 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

JEE Main 20255 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

JEE Main 202426 questions

  1. 4 Apr 2024, Shift 1 · Q6Let f:R→Rf: \mathbf{R} \to \mathbf{R} be a function given by…MediumSingle correct
  2. 4 Apr 2024, Shift 2 · Q8If the function f(x)={72x−9x−8x+12−1+cos⁡x,x≠0alog⁡e2log⁡e3,x=0f(x)=\begin{cases}\dfrac{72^x-9^x-8^x+1}{\sqrt2-\sqrt{1+\cos x}}, & x\ne 0\\ a\log_e 2\log_e 3, & x=0\end{cases} is…HardSingle correct
  3. 4 Apr 2024, Shift 2 · Q25Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a thrice differentiable function such that f(0)=0,f(1)=1,f(2)=−1,f(3)=2f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=−2f(4)=-2. Then, the…HardNumerical value
  4. 5 Apr 2024, Shift 1 · Q7If the function f(x)=sin⁡3x+αsin⁡x−βcos⁡3xx3f(x)=\frac{\sin3x+\alpha\sin x-\beta\cos3x}{x^3}, x∈Rx\in\mathbb{R}, is continuous at x=0x=0, then f(0)f(0) is equal to :MediumSingle correct
  5. 5 Apr 2024, Shift 1 · Q8Let f(x)=x5+2x3+3x+1f(x)=x^5+2x^3+3x+1, x∈Rx\in\mathbb{R}, and g(x)g(x) be a function such that g(f(x))=xg(f(x))=x for all x∈Rx\in\mathbb{R}. Then…MediumSingle correct
  6. 5 Apr 2024, Shift 2 · Q10Let f:[−1,2]→Rf : [-1, 2] \to \mathbf{R} be given by f(x)=2x2+x+[x2]−[x]f(x) = 2x^2 + x + [x^2] - [x], where [t][t] denotes the greatest integer less than or equal…MediumSingle correct
  7. 5 Apr 2024, Shift 2 · Q20If y(θ)=2cos⁡θ+cos⁡2θcos⁡3θ+4cos⁡2θ+5cos⁡θ+2y(\theta) = \frac{2\cos\theta + \cos 2\theta}{\cos 3\theta + 4\cos 2\theta + 5\cos\theta + 2}, then at θ=π2\theta = \frac{\pi}{2},…HardSingle correct
  8. 6 Apr 2024, Shift 1 · Q8If f(x)={x3sin⁡(1x),x≠00,x=0f(x)=\begin{cases} x^3\sin\left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases}, thenMediumSingle correct
  9. 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
  10. 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
  11. 8 Apr 2024, Shift 2 · Q9For a,b>0a, b > 0, let…HardSingle correct
  12. 9 Apr 2024, Shift 1 · Q24Let f:(0,π)→Rf:(0,\pi)\to\mathbf{R} be a function given by…HardNumerical value
  13. 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
  14. 1 Feb 2024, Shift 1 · Q8Let f:R→Rf:\mathbb{R}\to\mathbb{R} be defined as :…MediumSingle correct
  15. 1 Feb 2024, Shift 2 · Q8Let f(x)=∣2x2+5∣x∣−3∣f(x)=|2x^2+5|x|-3|, x∈Rx\in\mathbf{R}. If mm and nn denote the number of points where ff is not continuous and not differentiable…MediumSingle correct
  16. 1 Feb 2024, Shift 2 · Q25If y=(x+1)(x2−x)xx+x+x+115(3cos⁡2x−5)cos⁡3xy=\frac{(\sqrt{x}+1)(x^2-\sqrt{x})}{x\sqrt{x}+x+\sqrt{x}}+\frac{1}{15}(3\cos^2x-5)\cos^3x, then 96 y′(π6)96\,y'\left(\frac{\pi}{6}\right) is…HardNumerical value
  17. 27 Jan 2024, Shift 1 · Q8Consider the function.…HardSingle correct
  18. 27 Jan 2024, Shift 1 · Q23Let for a differentiable function f:(0,∞)→Rf:(0,\infty)\to\mathbf{R}, f(x)−f(y)≥log⁡e(xy)+x−yf(x)-f(y)\geq \log_e\left(\dfrac{x}{y}\right)+x-y,…HardNumerical value
  19. 27 Jan 2024, Shift 1 · Q25Let f(x)=x3+x2f′(1)+xf′′(2)+f′′′(3)f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3), x∈Rx\in\mathbf{R}. Then f′(10)f'(10) is equal to ________.MediumNumerical value
  20. 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
  21. 30 Jan 2024, Shift 1 · Q30If the function f(x)={1∣x∣,∣x∣≥2ax2+2b,∣x∣<2f(x)=\begin{cases}\frac{1}{|x|}, & |x|\geq2\\ ax^2+2b, & |x|<2\end{cases} is differentiable on R\mathbf{R}, then…MediumNumerical value
  22. 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
  23. 30 Jan 2024, Shift 2 · Q8Let aa and bb be real constants such that the function ff defined by…MediumSingle correct
  24. 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
  25. 31 Jan 2024, Shift 2 · Q8Differentiability of Modulus Functions · Medium · Single correct
  26. 31 Jan 2024, Shift 2 · Q9Open the question · Hard · Single correct

JEE Main 202310 questions

  1. 6 Apr 2023, Shift 1 · Q9Logarithmic Differentiation of Composite Products · Medium · Single correct
  2. 6 Apr 2023, Shift 1 · Q25Continuity involving GIF and Fractional Part · Hard · Numerical value
  3. 8 Apr 2023, Shift 1 · Q19Second Derivative of Composite Functions · Hard · Single correct
  4. 8 Apr 2023, Shift 2 · Q25Finding Unknowns using Differentiability · Medium · Numerical value
  5. 10 Apr 2023, Shift 1 · Q27Differentiability of Modulus Functions · Hard · Numerical value
  6. 11 Apr 2023, Shift 1 · Q7Continuity involving GIF and Fractional Part · Medium · Single correct
  7. 11 Apr 2023, Shift 2 · Q10Continuity and Differentiability of Composite Functions · Medium · Single correct
  8. 12 Apr 2023, Shift 1 · Q25Continuity involving GIF and Fractional Part · Medium · Numerical value
  9. 13 Apr 2023, Shift 1 · Q1Differentiating Functional Equations · Medium · Single correct
  10. 15 Apr 2023, Shift 1 · Q9Differentiability of Max/Min Functions · Hard · Single correct

JEE Main 202231 questions

  1. 25 Jul 2022, Shift 1 · Q26Piecewise Differentiability · Hard · Numerical value
  2. 25 Jul 2022, Shift 2 · Q24Extrema Involving Greatest Integer Function · Medium · Numerical value
  3. 26 Jul 2022, Shift 1 · Q1Differentiability via Functional Equations · Medium · Single correct
  4. 26 Jul 2022, Shift 1 · Q7Finding Unknown Constants for Continuity · Medium · Single correct
  5. 26 Jul 2022, Shift 1 · Q8Finding Unknown Constants for Continuity · Medium · Single correct
  6. 26 Jul 2022, Shift 2 · Q8Derivative of Variable Base Logarithms · Medium · Single correct
  7. 27 Jul 2022, Shift 1 · Q20Piecewise Differentiability · Hard · Single correct
  8. 27 Jul 2022, Shift 2 · Q5Continuity at a Point · Medium · Single correct
  9. 27 Jul 2022, Shift 2 · Q6Differentiability of Modulus Functions · Medium · Two statements
  10. 27 Jul 2022, Shift 2 · Q26Implicit Chain Rule · Hard · Numerical value
  11. 28 Jul 2022, Shift 1 · Q29e-Power Shortcut for 1^infinity Forms · Hard · Numerical value
  12. 28 Jul 2022, Shift 2 · Q65Functions Defined by Infinite Limits · Hard · Single correct
  13. 28 Jul 2022, Shift 2 · Q68Chain Rule in Parametric Differentiation · Hard · Single correct
  14. 29 Jul 2022, Shift 1 · Q18Differentiability of Modulus Functions · Hard · Single correct
  15. 29 Jul 2022, Shift 2 · Q4Finding Unknown Constants for Continuity · Easy · Single correct
  16. 29 Jul 2022, Shift 2 · Q26Continuity involving GIF and Fractional Part · Hard · Numerical value
  17. 30 Jul 2022, Shift 2 · Q69Continuity at a Point · Hard · Single correct
  18. 30 Jul 2022, Shift 2 · Q70Higher Order Derivatives · Hard · Single correct
  19. 24 Jun 2022, Shift 1 · Q25Continuity involving GIF and Fractional Part · Hard · Numerical value
  20. 24 Jun 2022, Shift 2 · Q5Continuity involving GIF and Fractional Part · Hard · Single correct
  21. 24 Jun 2022, Shift 2 · Q17Existence of Higher Order Derivatives · Hard · Single correct
  22. 25 Jun 2022, Shift 1 · Q6Derivative of Inverse Functions via Chain Rule · Easy · Single correct
  23. 25 Jun 2022, Shift 2 · Q22Continuity and Differentiability of Composite Functions · Hard · Numerical value
  24. 26 Jun 2022, Shift 1 · Q7Continuity and Differentiability of Composite Functions · Hard · Single correct
  25. 26 Jun 2022, Shift 2 · Q5Differentiability of Max/Min Functions · Medium · Single correct
  26. 26 Jun 2022, Shift 2 · Q21Differentiability via Functional Equations · Hard · Numerical value
  27. 27 Jun 2022, Shift 1 · Q8Second Order Implicit Chain Rule · Medium · Single correct
  28. 27 Jun 2022, Shift 2 · Q26Logarithmic Differentiation for Power Towers · Hard · Numerical value
  29. 28 Jun 2022, Shift 1 · Q8Continuity involving GIF and Fractional Part · Hard · Single correct
  30. 28 Jun 2022, Shift 2 · Q6Continuity and Differentiability of Composite Functions · Hard · Single correct
  31. 29 Jun 2022, Shift 1 · Q4Piecewise Differentiability · Hard · Single correct

JEE Main 202131 questions

  1. 3 Aug 2021, Shift 1 · Q66Finding Unknowns using Continuity · Medium · Single correct
  2. 3 Aug 2021, Shift 1 · Q89Recognizing the Derivative Definition · Easy · Numerical value
  3. 3 Aug 2021, Shift 2 · Q69Finding Unknown Constants for Continuity · Medium · Single correct
  4. 4 Aug 2021, Shift 1 · Q89Differentiability of Modulus Functions · Medium · Numerical value
  5. 4 Aug 2021, Shift 2 · Q67Differentiability via Functional Equations · Easy · Single correct
  6. 26 Aug 2021, Shift 1 · Q82Continuity at a Point · Medium · Numerical value
  7. 26 Aug 2021, Shift 1 · Q86Second Order Implicit Chain Rule · Medium · Numerical value
  8. 26 Aug 2021, Shift 2 · Q76Differentiability of Max/Min Functions · Medium · Single correct
  9. 27 Aug 2021, Shift 1 · Q84Second Order Implicit Chain Rule · Hard · Numerical value
  10. 27 Aug 2021, Shift 2 · Q67Periodic Reduction of tan-1(tan x) and cot-1(cot x) · Medium · Single correct
  11. 31 Aug 2021, Shift 1 · Q68Finding Unknown Constants for Continuity · Medium · Single correct
  12. 31 Aug 2021, Shift 1 · Q69Differentiability of Modulus Functions · Medium · Single correct
  13. 24 Feb 2021, Shift 1 · Q69Continuity involving GIF and Fractional Part · Medium · Single correct
  14. 25 Feb 2021, Shift 1 · Q86Differentiability of Modulus Functions · Medium · Numerical value
  15. 25 Feb 2021, Shift 2 · Q81Differentiability of Max/Min Functions · Hard · Numerical value
  16. 26 Feb 2021, Shift 1 · Q74Differentiability via Functional Equations · Medium · Single correct
  17. 26 Feb 2021, Shift 2 · Q68LHD and RHD Calculation · Easy · Single correct
  18. 26 Feb 2021, Shift 2 · Q77Finding Unknown Constants for Continuity · Medium · Single correct
  19. 22 Jul 2021, Shift 2 · Q65Limits via Series Expansion for Continuity · Hard · Single correct
  20. 22 Jul 2021, Shift 2 · Q85Piecewise Differentiability · Hard · Numerical value
  21. 25 Jul 2021, Shift 1 · Q64Continuity and Differentiability of Integral Functions · Medium · Single correct
  22. 25 Jul 2021, Shift 1 · Q65Continuity at a Point · Medium · Single correct
  23. 25 Jul 2021, Shift 2 · Q72Piecewise Differentiability · Medium · Single correct
  24. 25 Jul 2021, Shift 2 · Q90Finding Unknown Constants via Continuity · Medium · Numerical value
  25. 16 Mar 2021, Shift 2 · Q69Continuity involving GIF and Fractional Part · Hard · Single correct
  26. 16 Mar 2021, Shift 2 · Q85Continuity and Differentiability of Composite Functions · Medium · Numerical value
  27. 17 Mar 2021, Shift 1 · Q84Limits via Series Expansion for Continuity · Medium · Numerical value
  28. 17 Mar 2021, Shift 1 · Q89Pre-simplification via Trig Substitution · Hard · Numerical value
  29. 18 Mar 2021, Shift 1 · Q70Finding Unknowns using Differentiability · Medium · Single correct
  30. 18 Mar 2021, Shift 2 · Q72Finding Unknown Constants for Continuity · Medium · Single correct · has a figure
  31. 18 Mar 2021, Shift 2 · Q90Differentiability via Functional Equations · Medium · Numerical value

JEE Main 202019 questions

  1. 8 Jan 2020, Shift 1 · Q58Modulus Traps in Trigonometric Functions · Hard · Single correct
  2. 8 Jan 2020, Shift 1 · Q59Logarithmic Function Application · Medium · Single correct
  3. 8 Jan 2020, Shift 2 · Q59Proving Inequalities via LMVT · Hard · Single correct
  4. 9 Jan 2020, Shift 1 · Q58Continuity at a Point · Medium · Single correct
  5. 9 Jan 2020, Shift 1 · Q60Proving Inequalities via LMVT · Hard · Single correct
  6. 9 Jan 2020, Shift 2 · Q58Continuity involving GIF and Fractional Part · Medium · Single correct
  7. 9 Jan 2020, Shift 2 · Q60Derivative of Inverse Functions via Chain Rule · Easy · Single correct
  8. 2 Sep 2020, Shift 1 · Q59Continuity at a Point · Medium · Single correct
  9. 2 Sep 2020, Shift 2 · Q72Pre-simplification via Trig Substitution · Hard · Numerical value
  10. 3 Sep 2020, Shift 1 · Q57Second Order Implicit Chain Rule · Medium · Single correct
  11. 4 Sep 2020, Shift 1 · Q59Implicit Chain Rule · Medium · Single correct
  12. 4 Sep 2020, Shift 1 · Q73Differentiability via Functional Equations · Medium · Numerical value
  13. 4 Sep 2020, Shift 2 · Q58Differentiability via Functional Equations · Hard · Single correct
  14. 4 Sep 2020, Shift 2 · Q59Piecewise Differentiability · Medium · Single correct
  15. 4 Sep 2020, Shift 2 · Q70Open the question · Easy · Single correct
  16. 5 Sep 2020, Shift 1 · Q59Existence of Higher Order Derivatives · Medium · Single correct
  17. 5 Sep 2020, Shift 1 · Q73Continuity involving GIF and Fractional Part · Medium · Numerical value
  18. 6 Sep 2020, Shift 2 · Q57Rolle's Theorem for Second Derivative · Medium · Single correct
  19. 6 Sep 2020, Shift 2 · Q58Differentiability of Max/Min Functions · Easy · Single correct

JEE Main 20171 question

  1. 2 Apr 2017 (offline) · Q71tan^-1(2x/(1-x^2)) Piecewise Conversion · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

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