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Sunday, 25 October

JEE Main · Maths · Class 12

Application of Derivatives: JEE Main previous year questions

148 questions in 90 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
148
in 90 of 108 shifts · 8 of 8 years
Average a shift
1.2
of 25 Maths · 0.8 since 2024 -0.7
Typical range
0.6–1.7
questions a shift; fewest 0.3, most 1.7
Weighted estimate
0.9
model, recent years count more · about 3.7 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 Application of Derivatives

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
148in 90 of 108 shifts
Study plan gives it
18 hover 12 months; 13 h over 6
Study this chapter →

Ideas asked most often

  1. Optimization Problems13×
  2. Closed Interval Extrema8×
  3. Finding Intervals7×
  4. Analyzing Polynomial Roots via Extrema6×
  5. Equation of Normal6×

217 of the 311 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, 42% 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

Application of Derivatives at a glance

  1. 01

    58%

    of its 31 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

    70%

    of the 311 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    26%

    of its questions asked for a numerical answer, 0.9 times the Maths average.

  4. 04

    21%

    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.

0241.7’171.7’201.5’211.5’220.6’231’240.9’250.3’26

Raw count: 2017: 2 in 1 shift · 2020: 20 in 12 shifts · 2021: 42 in 24 shifts · 2022: 43 in 24 shifts · 2023: 9 in 12 shifts · 2024: 22 in 18 shifts · 2025: 7 in 8 shifts · 2026: 3 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step52%
  • Numerical answer26%
  • Application10%
  • Calculation6%
  • Two statements3%
  • Conceptual2%
  • Recall, single correct1%

Most common asks: count real roots of polynomial equation (5); maximum area of inscribed figure (2); maximise area of inscribed figure (2).

Profile

This chapter in numbers

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

Rank, all JEE chapters
#42
of 70 by weighted estimate
Rank in Maths
#15
of 21 chapters
Share of Maths
4.6%
of its questions, all shifts analysed
Busiest year
2017
1.7 questions a shift
Year to year
Some swing
varies by about 0.5 questions a shift
Long-run direction
-0.15
questions a shift, per year
Easy questions
7%
21% rated hard
Numerical answer
26%
0.9× the Maths rate
With a figure
1%
graph, diagram or structure
Study time
18 h
13 h on a 6-month plan
Marks per study hour
0.21
#61 of 70 chapters
Foundation for others
68%
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).

  • 20172
  • 202020
  • 202142
  • 202243
  • 20239
  • 202422
  • 20257
  • 20263
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step76%
  • Application14%
  • Calculation8%
  • Conceptual2%
  • Recall1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 311 ideas. In the 108 shifts analysed, JEE Main built a question around 70 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
70
Touched on in a question
24
Never asked
217

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. 2 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
020+questions in that year’s analysed shifts, shaded per shift
  • Maxima and Minima

    As a topic: 80 questions in 8 of 8 years, most often single correct, 26% numerical answer. Recent asks: integer values for trigonometric equation solvability; numerical: max of trig expression on interval; determine polynomial from extrema and limit.

  • Tangents and Normals

    As a topic: 36 questions in 6 of 8 years, most often single correct, 36% numerical answer.

  • Monotonicity

    As a topic: 23 questions in 6 of 8 years, most often single correct, 4% numerical answer.

  • Chain Rule

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

  • Open73 · 49%8192041263

    29 ideas inside

    • OpenRepeated12 · 16%55
    • OpenRepeated8 · 11%3
    • OpenRepeated5 · 7%3
    • OpenRepeated5 · 7%22
    • OpenRepeated4 · 5%2
    • OpenRepeated4 · 5%2
    • OpenRepeated3 · 4%
    • Open3 · 4%3
    • OpenRepeated3 · 4%
    • Open3 · 4%3
    • OpenRepeated3 · 4%
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open25 · 17%6107
  • Open23 · 16%27724
  • Open7 · 5%23
  • Open7 · 5%33
  • Open4 · 3%22
  • Open3 · 2%2
  • Open1 · 1%
  • Open1 · 1%
  • Open1 · 1%
  • Open1 · 1%
  • 9 Apr ’24 S1 · Q6
    Let f(x)=ax3+bx2+cx+41f(x)=ax^3+bx^2+cx+41 be such that f(1)=40f(1)=40, f′(1)=2f'(1)=2 and f′′(1)=4f''(1)=4. Then a2+b2+c2a^2+b^2+c^2 is equal to :

    easySingle correct

  • 17 Mar ’21 S1 · Q81
    Read the question

    mediumNumerical value

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, 66 different ideas were tested; 30 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 148 Application of Derivatives 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 20263 questions

  1. 2 Apr 2026, Shift 1 · Q18The number of critical points of the function f(x)={∣sin⁡xx∣,x≠01,x=0f(x)=\begin{cases}\left|\frac{\sin x}{x}\right|, & x\neq0\\ 1, & x=0\end{cases} in the…HardSingle correct
  2. 2 Apr 2026, Shift 2 · Q18Let f(x)f(x) be a polynomial of degree 5, and have extrema at x=1x = 1 and x=−1x = -1. If lim⁡x→0(f(x)x3)=−5\lim_{x \to 0}\left(\frac{f(x)}{x^3}\right) = -5,…MediumSingle correct
  3. 4 Apr 2026, Shift 2 · Q12max⁡0≤x≤π(16sin⁡(x2)cos⁡3(x2))\max_{0\le x\le\pi}\left(16\sin\left(\frac x2\right)\cos^3\left(\frac x2\right)\right) is equal to:MediumSingle correct

JEE Main 20257 questions

  1. 2 Apr 2025, Shift 1 · Q8If the function f(x)=2x3−9ax2+12a2x+1f(x)=2x^3-9ax^2+12a^2x+1, where a>0a>0, attains its local maximum and local minimum values at p and q, respectively, such…MediumSingle correct
  2. 3 Apr 2025, Shift 2 · Q16Let f:R→Rf: \mathrm{R} \to \mathrm{R} be a function defined by f(x)=∣∣x+2∣−2∣x∣∣f(x) = \left||x+2| - 2|x|\right|. If mm is the number of points of local…MediumSingle correct
  3. 3 Apr 2025, Shift 2 · Q17The shortest distance between the curves y2=8xy^2 = 8x and x2+y2+12y+35=0x^2 + y^2 + 12y + 35 = 0 is:MediumSingle correct
  4. 4 Apr 2025, Shift 2 · Q17Let a>0a>0. If the function f(x)=6x3−45ax2+108a2x+1f(x)=6x^3-45ax^2+108a^2x+1 attains its local maximum and minimum values at the points x1x_1 and x2x_2…MediumSingle correct
  5. 7 Apr 2025, Shift 1 · Q17Let x=−1x = -1 and x=2x = 2 be the critical points of the function f(x)=x3+ax2+blog⁡e∣x∣+1f(x) = x^3 + ax^2 + b\log_e|x| + 1, x≠0x \neq 0. Let mm and MM…MediumSingle correct
  6. 7 Apr 2025, Shift 2 · Q18Let f:R→Rf:\mathbf{R}\to\mathbf{R} be a polynomial function of degree four having extreme values at x=4x=4 and x=5x=5. If…MediumSingle correct
  7. 8 Apr 2025, Shift 2 · Q17Let the function f(x)=x3+3x+3f(x) = \frac{x}{3} + \frac{3}{x} + 3, x≠0x \neq 0 be strictly increasing in…EasySingle correct

JEE Main 202422 questions

  1. 4 Apr 2024, Shift 1 · Q11Let f(x)=x5+2ex/4f(x)=x^5+2e^{x/4} for all x∈Rx \in \mathbf{R}. Consider a function g(x)g(x) such that (g∘f)(x)=x(g\circ f)(x)=x for all x∈Rx \in \mathbf{R}.…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q12Let the sum of the maximum and the minimum values of the function f(x)=2x2−3x+82x2+3x+8f(x)=\frac{2x^2-3x+8}{2x^2+3x+8} be mn\frac{m}{n}, where…MediumSingle correct
  3. 5 Apr 2024, Shift 1 · Q5For the function f(x)=sin⁡x+3x−2π(x2+x)f(x)=\sin x+3x-\frac{2}{\pi}(x^2+x), where x∈[0,π2]x\in\left[0,\frac{\pi}{2}\right], consider the following two statements :…MediumTwo statements
  4. 5 Apr 2024, Shift 1 · Q9Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides…HardSingle correct
  5. 6 Apr 2024, Shift 1 · Q9The interval in which the function f(x)=xxf(x)=x^x, x>0x>0, is strictly increasing isEasySingle correct
  6. 6 Apr 2024, Shift 2 · Q8If the function f(x)=(1x)2xf(x)=\left(\frac{1}{x}\right)^{2x} ; x>0x>0 attains the maximum value at x=1ex=\frac{1}{e} then :HardSingle correct
  7. 8 Apr 2024, Shift 1 · Q7For the function f(x)=(cos⁡x)−x+1f(x)=(\cos x)-x+1, x∈Rx\in\mathbb{R}, between the following two statements (S1) f(x)=0f(x)=0 for only one value of xx in…MediumTwo statements
  8. 8 Apr 2024, Shift 1 · Q8The number of critical points of the function f(x)=(x−2)2/3(2x+1)f(x)=(x-2)^{2/3}(2x+1) isMediumSingle correct
  9. 8 Apr 2024, Shift 1 · Q9Let f(x)=4cos⁡3x+33cos⁡2x−10f(x)=4\cos^3x+3\sqrt{3}\cos^2x-10. The number of points of local maxima of ff in interval (0,2π)(0,2\pi) isHardSingle correct
  10. 8 Apr 2024, Shift 2 · Q10If the function f(x)=2x3−9ax2+12a2x+1f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, a>0a > 0 has a local maximum at x=αx = \alpha and a local minimum at x=α2x = \alpha^2,…MediumSingle correct
  11. 8 Apr 2024, Shift 2 · Q24Let A be the region enclosed by the parabola y2=2xy^2 = 2x and the line x=24x = 24. Then the maximum area of the rectangle inscribed in the…MediumNumerical value
  12. 9 Apr 2024, Shift 1 · Q6Let f(x)=ax3+bx2+cx+41f(x)=ax^3+bx^2+cx+41 be such that f(1)=40f(1)=40, f′(1)=2f'(1)=2 and f′′(1)=4f''(1)=4. Then a2+b2+c2a^2+b^2+c^2 is equal to :EasySingle correct
  13. 9 Apr 2024, Shift 1 · Q27Let the set of all positive values of λ\lambda, for which the point of local minimum of the function (1+x(λ2−x2))(1+x(\lambda^2-x^2)) satisfies…MediumNumerical value
  14. 9 Apr 2024, Shift 2 · Q25Let the set of all values of pp, for which f(x)=(p2−6p+8)(sin⁡22x−cos⁡22x)+2(2−p)x+7f(x)=(p^2-6p+8)\left(\sin^2 2x-\cos^2 2x\right)+2(2-p)x+7 does not have any critical point,…MediumNumerical value
  15. 1 Feb 2024, Shift 1 · Q7If 5f(x)+4f(1x)=x2−2, ∀ x≠05f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0 and y=9x2f(x)y=9x^2f(x), then yy is strictly increasing in :HardSingle correct
  16. 29 Jan 2024, Shift 1 · Q10Consider the function f:[12,1]→Rf:\left[\frac{1}{2},1\right]\to\mathbb{R} defined by f(x)=42x3−32x−1f(x)=4\sqrt{2}x^3-3\sqrt{2}x-1. Consider the statements (I)…MediumTwo statements
  17. 29 Jan 2024, Shift 1 · Q24Let f(x)=2x−x2f(x)=2^x-x^2, x∈Rx\in\mathbb{R}. If mm and nn are respectively the number of points at which the curves y=f(x)y=f(x) and y=f′(x)y=f'(x)…MediumNumerical value
  18. 30 Jan 2024, Shift 1 · Q7The maximum area of a triangle whose one vertex is at (0,0)(0,0) and the other two vertices lie on the curve y=−2x2+54y=-2x^2+54 at points (x,y)(x,y)…MediumSingle correct
  19. 30 Jan 2024, Shift 1 · Q9Let g:R→Rg:\mathbf{R}\to\mathbf{R} be a non constant twice differentiable function such that…HardSingle correct
  20. 30 Jan 2024, Shift 2 · Q9Let f(x)=(x+3)2(x−2)3f(x) = (x+3)^2 (x-2)^3, x∈[−4,4]x \in [-4, 4]. If MM and mm are the maximum and minimum values of ff, respectively in [−4,4][-4, 4], then…MediumSingle correct
  21. 31 Jan 2024, Shift 1 · Q25Let S=(−1,∞)S=(-1,\infty) and f:S→Rf:S\to\mathbb{R} be defined as f(x)=∫−1x(et−1)11(2t−1)5(t−2)7(t−3)12(2t−10)61 dtf(x)=\int_{-1}^{x}(e^t-1)^{11}(2t-1)^5(t-2)^7(t-3)^{12}(2t-10)^{61}\,dt, Let p…HardNumerical value
  22. 31 Jan 2024, Shift 2 · Q1If the function f:(−∞,−1]→(a,b]f:(-\infty,-1]\to(a,b] defined by f(x)=ex3−3x+1f(x)=e^{x^3-3x+1} is one - one and onto, then the distance of the point…MediumSingle correct

JEE Main 20239 questions

  1. 6 Apr 2023, Shift 2 · Q24The number of points, where the curve y=x5−20x3+50x+2y=x^5-20x^3+50x+2 crosses the x-axis, is ________.MediumNumerical value
  2. 8 Apr 2023, Shift 1 · Q23If aαa_\alpha is the greatest term in the sequence an=n3n4+147a_n=\frac{n^3}{n^4+147}, n=1,2,3,…,n=1,2,3,\ldots, then α\alpha is equal to ____________.MediumNumerical value
  3. 10 Apr 2023, Shift 1 · Q7A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to…MediumSingle correct
  4. 10 Apr 2023, Shift 2 · Q9Let g(x)=f(x)+f(1−x)g(x) = f(x) + f(1-x) and f′′(x)>0, x∈(0,1)f''(x) > 0,\ x \in (0,1). If gg is decreasing in the interval (0,α)(0, \alpha) and increasing in the…HardSingle correct
  5. 10 Apr 2023, Shift 2 · Q25Let the quadratic curve passing through the point (−1,0)(-1, 0) and touching the line y=xy = x at (1,1)(1, 1) be y=f(x)y = f(x). Then the…MediumNumerical value
  6. 11 Apr 2023, Shift 1 · Q10Let f:[2,4]→Rf : [2, 4] \to \mathbb{R} be a differentiable function such that (xlog⁡ex)f′(x)+(log⁡ex)f(x)+f(x)≥1, x∈[2,4](x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]…HardTwo statements
  7. 11 Apr 2023, Shift 2 · Q24The number of points, where the curve f(x)=e8x−e6x−3e4x−e2x+1f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1, x∈Rx \in \mathbb{R} cuts xx-axis, is equal to…MediumNumerical value
  8. 12 Apr 2023, Shift 1 · Q9If the local maximum value of the function f(x)=(3e2sin⁡x)sin⁡2xf(x)=\left(\frac{\sqrt{3e}}{2\sin x}\right)^{\sin^2 x}, x∈(0,π2)x\in\left(0,\frac{\pi}{2}\right),…HardSingle correct
  9. 13 Apr 2023, Shift 1 · Q10Closed Interval Extrema · Hard · Single correct

JEE Main 202243 questions

  1. 25 Jul 2022, Shift 1 · Q6Closed Interval Extrema · Medium · Single correct
  2. 25 Jul 2022, Shift 1 · Q7First Derivative Test · Medium · Single correct
  3. 25 Jul 2022, Shift 2 · Q29Area of Triangle Formed by Tangent and Normal · Hard · Numerical value
  4. 26 Jul 2022, Shift 1 · Q9Extrema at Piecewise Junctions · Medium · Single correct
  5. 26 Jul 2022, Shift 1 · Q24Analyzing Polynomial Roots via Extrema · Hard · Numerical value
  6. 26 Jul 2022, Shift 1 · Q29Parabola Normal Point Form · Hard · Numerical value
  7. 26 Jul 2022, Shift 2 · Q5Shortest Distance Between Curves · Hard · Single correct
  8. 27 Jul 2022, Shift 1 · Q26Tangents Parallel to Coordinate Axes · Medium · Numerical value
  9. 27 Jul 2022, Shift 2 · Q25Chain Rule in Related Rates · Medium · Numerical value
  10. 28 Jul 2022, Shift 1 · Q17Optimization via AM-GM Inequality · Medium · Single correct
  11. 28 Jul 2022, Shift 1 · Q20LDEs Formed via Leibniz Integral Rule · Hard · Single correct
  12. 28 Jul 2022, Shift 1 · Q23Higher-Order Derivative Roots · Medium · Numerical value
  13. 28 Jul 2022, Shift 2 · Q66Finding Intervals · Medium · Single correct
  14. 28 Jul 2022, Shift 2 · Q67Closed Interval Extrema · Medium · Single correct
  15. 29 Jul 2022, Shift 1 · Q20Points of Inflection · Hard · Other
  16. 29 Jul 2022, Shift 2 · Q27Common Tangents to Two Curves · Medium · Numerical value
  17. 30 Jul 2022, Shift 2 · Q83Analyzing Polynomial Roots via Extrema · Medium · Numerical value
  18. 30 Jul 2022, Shift 2 · Q84Optimization Problems · Medium · Numerical value · has a figure
  19. 24 Jun 2022, Shift 1 · Q3Chain Rule in Related Rates · Medium · Single correct
  20. 24 Jun 2022, Shift 1 · Q10First Derivative Test · Hard · Single correct
  21. 24 Jun 2022, Shift 1 · Q11Tangents Passing Through Origin · Medium · Single correct
  22. 24 Jun 2022, Shift 1 · Q12Closed Interval Extrema · Hard · Single correct
  23. 24 Jun 2022, Shift 2 · Q11Polynomial Root Counting · Medium · Single correct
  24. 24 Jun 2022, Shift 2 · Q20Parameter Range for Global Monotonicity · Medium · Single correct
  25. 25 Jun 2022, Shift 1 · Q12Trigonometric Monotonicity by Quadrant · Hard · Single correct
  26. 25 Jun 2022, Shift 1 · Q13Monotonicity of Composite Functions · Hard · Single correct
  27. 25 Jun 2022, Shift 2 · Q11Chain Rule in Related Rates · Medium · Single correct
  28. 25 Jun 2022, Shift 2 · Q14Tangents to Parametric Curves · Medium · Single correct
  29. 25 Jun 2022, Shift 2 · Q28Extrema of Modulus Functions · Hard · Numerical value
  30. 26 Jun 2022, Shift 1 · Q8Extrema of Absolute Value Functions · Medium · Single correct
  31. 26 Jun 2022, Shift 1 · Q9Tangents to Implicit Curves · Medium · Single correct
  32. 26 Jun 2022, Shift 2 · Q6Optimization Problems · Hard · Single correct
  33. 27 Jun 2022, Shift 1 · Q6Analyzing Polynomial Roots via Extrema · Medium · Single correct
  34. 27 Jun 2022, Shift 1 · Q7Optimization Problems · Medium · Single correct
  35. 27 Jun 2022, Shift 2 · Q7Extrema of Integral Functions · Medium · Single correct
  36. 28 Jun 2022, Shift 1 · Q12Counting Roots using Monotonicity · Medium · Single correct
  37. 28 Jun 2022, Shift 1 · Q22Exponential Reducible to Quadratic · Hard · Numerical value
  38. 28 Jun 2022, Shift 1 · Q26Normals Passing Through a Given Point · Medium · Numerical value
  39. 29 Jun 2022, Shift 1 · Q14Optimization Problems · Medium · Single correct
  40. 29 Jun 2022, Shift 2 · Q6First Derivative Test · Medium · Single correct
  41. 29 Jun 2022, Shift 2 · Q26Auxiliary Functions: Product and Quotient Rules · Hard · Numerical value
  42. 30 Jun 2022, Shift 1 · Q8Optimization Problems · Medium · Single correct
  43. 30 Jun 2022, Shift 1 · Q9Finding Intervals · Easy · Single correct

JEE Main 202142 questions

  1. 3 Aug 2021, Shift 1 · Q67Constant Sum of Intercepts · Medium · Single correct
  2. 3 Aug 2021, Shift 2 · Q70Proving Lipschitz Condition via LMVT · Medium · Single correct
  3. 3 Aug 2021, Shift 2 · Q71Finding Parameters from Given Extrema · Medium · Single correct
  4. 4 Aug 2021, Shift 1 · Q68Equation of Normal · Easy · Single correct
  5. 4 Aug 2021, Shift 1 · Q70Equation of Tangent · Medium · Single correct
  6. 4 Aug 2021, Shift 1 · Q85Second Derivative Test · Easy · Numerical value
  7. 4 Aug 2021, Shift 2 · Q68Tangents to Piecewise/Modulus Functions · Medium · Single correct
  8. 4 Aug 2021, Shift 2 · Q87Second Derivative Test · Medium · Numerical value
  9. 26 Aug 2021, Shift 1 · Q84Optimization Problems · Medium · Numerical value
  10. 26 Aug 2021, Shift 2 · Q66Extrema of Variable-Base Exponentials · Medium · Single correct
  11. 27 Aug 2021, Shift 1 · Q66Optimization Problems · Medium · Single correct
  12. 27 Aug 2021, Shift 1 · Q85Analyzing Polynomial Roots via Extrema · Medium · Numerical value
  13. 27 Aug 2021, Shift 2 · Q68Extrema of Trigonometric Compositions · Medium · Single correct
  14. 27 Aug 2021, Shift 2 · Q69Optimization Problems · Medium · Single correct
  15. 31 Aug 2021, Shift 1 · Q83Parameter Range for Localized Monotonicity · Easy · Numerical value
  16. 31 Aug 2021, Shift 2 · Q66Angle Between Curves · Medium · Single correct
  17. 31 Aug 2021, Shift 2 · Q68Higher-Order Derivative Roots · Medium · Single correct
  18. 31 Aug 2021, Shift 2 · Q85Determining Coefficients from Extrema · Medium · Numerical value
  19. 24 Feb 2021, Shift 1 · Q67First Derivative Test · Medium · Single correct
  20. 24 Feb 2021, Shift 1 · Q75Tangent Intersecting Curve Again · Medium · Single correct
  21. 24 Feb 2021, Shift 2 · Q63Shortest Distance Between Curves · Medium · Single correct
  22. 24 Feb 2021, Shift 2 · Q70Equation of Tangent · Easy · Single correct
  23. 24 Feb 2021, Shift 2 · Q73Monotonicity in Piecewise Functions · Medium · Single correct
  24. 25 Feb 2021, Shift 1 · Q65Parameter Evaluation · Medium · Single correct
  25. 25 Feb 2021, Shift 1 · Q72Orthogonal Intersection of Curves · Medium · Single correct
  26. 25 Feb 2021, Shift 1 · Q87Critical vs Stationary Points · Hard · Numerical value
  27. 25 Feb 2021, Shift 2 · Q67Optimization via AM-GM Inequality · Medium · Single correct
  28. 25 Feb 2021, Shift 2 · Q85Orthogonal Intersection of Curves · Medium · Numerical value
  29. 26 Feb 2021, Shift 1 · Q68Second Derivative Test · Medium · Single correct
  30. 26 Feb 2021, Shift 2 · Q75Standard Geometric Optimization Results · Easy · Single correct
  31. 26 Feb 2021, Shift 2 · Q83Equation of Normal · Medium · Numerical value
  32. 26 Feb 2021, Shift 2 · Q84Polynomial Root Counting · Medium · Numerical value
  33. 22 Jul 2021, Shift 2 · Q75Monotonicity in Piecewise Functions · Medium · Single correct
  34. 25 Jul 2021, Shift 1 · Q67Finding Intervals · Medium · Single correct
  35. 25 Jul 2021, Shift 2 · Q89Optimization Problems · Medium · Numerical value · has a figure
  36. 16 Mar 2021, Shift 2 · Q64Finding Intervals · Medium · Single correct
  37. 16 Mar 2021, Shift 2 · Q79Differentiating Functional Equations · Hard · Single correct
  38. 17 Mar 2021, Shift 1 · Q81Open the question · Medium · Numerical value
  39. 17 Mar 2021, Shift 2 · Q69First Derivative Test · Hard · Single correct
  40. 17 Mar 2021, Shift 2 · Q85Closed Interval Extrema · Medium · Numerical value
  41. 18 Mar 2021, Shift 2 · Q68Optimization Problems · Hard · Single correct
  42. 18 Mar 2021, Shift 2 · Q85Determining Coefficients from Extrema · Medium · Numerical value

JEE Main 202020 questions

  1. 8 Jan 2020, Shift 1 · Q74Tangents to Implicit Curves · Medium · Numerical value
  2. 8 Jan 2020, Shift 2 · Q60Equation of Normal · Medium · Single correct
  3. 8 Jan 2020, Shift 2 · Q73Determining Coefficients from Extrema · Medium · Numerical value
  4. 9 Jan 2020, Shift 1 · Q59Chain Rule in Related Rates · Medium · Single correct
  5. 9 Jan 2020, Shift 2 · Q61Extrema of Integral Functions · Medium · Single correct
  6. 2 Sep 2020, Shift 1 · Q60Tangents to Implicit Curves · Medium · Single correct
  7. 2 Sep 2020, Shift 1 · Q61Determining Coefficients from Extrema · Medium · Single correct
  8. 2 Sep 2020, Shift 1 · Q64Equation of Normal · Medium · Single correct
  9. 2 Sep 2020, Shift 2 · Q60Equation of Normal · Medium · Single correct
  10. 2 Sep 2020, Shift 2 · Q61First Derivative Test · Medium · Single correct
  11. 3 Sep 2020, Shift 1 · Q59Finding Intervals · Medium · Single correct
  12. 3 Sep 2020, Shift 2 · Q58Analyzing Polynomial Roots via Extrema · Medium · Single correct
  13. 3 Sep 2020, Shift 2 · Q59Chain Rule in Related Rates · Easy · Single correct
  14. 3 Sep 2020, Shift 2 · Q74Intercepts of Tangent and Normal · Medium · Numerical value
  15. 4 Sep 2020, Shift 1 · Q58Proving Inequalities via LMVT · Hard · Single correct
  16. 4 Sep 2020, Shift 2 · Q60Optimization via AM-GM Inequality · Medium · Single correct
  17. 4 Sep 2020, Shift 2 · Q62Inscribed 2D Geometry Optimization · Medium · Single correct
  18. 5 Sep 2020, Shift 1 · Q60Shortest Distance from Point to Curve · Medium · Single correct
  19. 6 Sep 2020, Shift 2 · Q59Finding the Mean Value Point · Medium · Single correct
  20. 6 Sep 2020, Shift 2 · Q60First Derivative Test · Hard · Single correct

JEE Main 20172 questions

  1. 2 Apr 2017 (offline) · Q72Equation of Normal · Medium · Single correct
  2. 2 Apr 2017 (offline) · Q73Optimization Problems · 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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