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Sunday, 25 October

JEE Main · Maths · Class 12

Integrals: JEE Main previous year questions

211 questions in 108 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
211
in 108 of 108 shifts · 8 of 8 years
Average a shift
1.7
of 25 Maths · 1.7 since 2024 0.0
Typical range
1.6–1.9
questions a shift; fewest 1.6, most 1.9
Weighted estimate
1.7
model, recent years count more · about 6.7 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 Integrals

Priority

Must do

One of the 8 Maths chapters that together held the first half of Maths questions in the 108 shifts analysed. How bands are set

Past questions
211in 108 of 108 shifts
Study plan gives it
29 hover 12 months; 22 h over 6
Study this chapter →

Ideas asked most often

  1. Greatest Integer Function Integrals29×
  2. King's Property18×
  3. Symmetric Limits with Exponential Denominator Trick10×
  4. Summation to Riemann Form9×
  5. Periodic Function Property6×

220 of the 314 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, 13% 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

Integrals at a glance

  1. 01

    87%

    of its 62 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 314 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    28%

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

  4. 04

    48%

    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.

0241.7’171.8’201.9’211.6’221.6’231.9’241.6’251.6’26

Raw count: 2017: 2 in 1 shift · 2020: 21 in 12 shifts · 2021: 54 in 24 shifts · 2022: 45 in 24 shifts · 2023: 22 in 12 shifts · 2024: 40 in 18 shifts · 2025: 13 in 8 shifts · 2026: 14 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step45%
  • Numerical answer28%
  • Calculation19%
  • Application8%

Most common asks: definite integral with greatest integer function (25); definite integral using king's property (18); limit of sum as definite integral (5).

Profile

This chapter in numbers

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

Rank, all JEE chapters
#6
of 70 by weighted estimate
Rank in Maths
#4
of 21 chapters
Share of Maths
6.8%
of its questions, all shifts analysed
Busiest year
2021
1.9 questions a shift
Year to year
Steady
varies by about 0.1 questions a shift
Long-run direction
-0.02
questions a shift, per year
Easy questions
5%
48% rated hard
Numerical answer
28%
0.9× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
29 h
22 h on a 6-month plan
Marks per study hour
0.23
#43 of 70 chapters
Foundation for others
62%
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
  • 202021
  • 202154
  • 202245
  • 202322
  • 202440
  • 202513
  • 202614
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step63%
  • Calculation29%
  • Application8%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 314 ideas. In the 108 shifts analysed, JEE Main built a question around 65 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
65
Touched on in a question
29
Never asked
220

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

’17’20’21’22’23’24’25’26
031+questions in that year’s analysed shifts, shaded per shift
  • Definite Integral Properties

    As a topic: 100 questions in 7 of 8 years, most often single correct, 28% numerical answer. Recent asks: definite integral with exponential denominator trick; integrate rational function then evaluate logs; numerical: improper definite integral value.

  • Integration by Substitution

    As a topic: 51 questions in 8 of 8 years, most often single correct, 31% numerical answer.

  • Integration by Parts

    As a topic: 14 questions in 7 of 8 years, most often single correct, 21% numerical answer.

  • Integral as Limit of Sum

    As a topic: 13 questions in 4 of 8 years, most often single correct, 15% 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.

  • Open100 · 47%8312171977

    19 ideas inside

    • OpenRepeated29 · 29%1183222
    • OpenRepeated18 · 18%24272
    • OpenRepeated10 · 10%233
    • OpenRepeated6 · 6%23
    • OpenRepeated6 · 6%4
    • OpenRepeated6 · 6%3
    • OpenRepeated4 · 4%2
    • OpenRepeated4 · 4%2
    • OpenRepeated3 · 3%2
    • OpenRepeated2 · 2%
    • OpenRepeated2 · 2%
    • OpenRepeated2 · 2%
    • OpenRepeated2 · 2%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open50 · 24%714571132
  • Open14 · 7%32232
  • Open11 · 5%362
  • Open10 · 5%242
  • Open3 · 1%
  • Open2 · 1%
  • Open1 · 0%
  • Open1 · 0%

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; 35 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 211 Integrals 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 202614 questions

  1. 2 Apr 2026, Shift 1 · Q19Let [⋅][\cdot] denote the greatest integer function. Then the value of ∫03(ex+e−x[x]!)dx\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx is :MediumSingle correct
  2. 2 Apr 2026, Shift 1 · Q25If α=∫023log⁡2(x2+4)dx+∫242x−4 dx\alpha=\int_0^{2\sqrt3}\log_2\left(x^2+4\right)dx+\int_2^4\sqrt{2^x-4}\,dx, then α2\alpha^2 is equal to __________.HardNumerical value
  3. 2 Apr 2026, Shift 2 · Q17The value of ∫020π(sin⁡4x+cos⁡4x)dx\int_0^{20\pi} (\sin^4 x + \cos^4 x)dx is equal to:EasySingle correct
  4. 2 Apr 2026, Shift 2 · Q19Let f(x)=∫16x+24x2+2x−15dxf(x) = \int\frac{16x + 24}{x^2 + 2x - 15}dx. If f(4)=14log⁡6(3)f(4) = 14\log_6(3) and…MediumSingle correct
  5. 4 Apr 2026, Shift 1 · Q19Let ∫−22(∣sin⁡x∣+[xsin⁡x])dx=2(3−cos⁡2)+β\int_{-2}^{2}\left(|\sin x|+[x\sin x]\right)dx=2(3-\cos 2)+\beta, where [⋅][\cdot] is the greatest integer function. Then…HardSingle correct
  6. 4 Apr 2026, Shift 2 · Q4If α=1\alpha=1 and β=1+i2\beta=1+i\sqrt{2}, where i=−1i=\sqrt{-1} are two roots of the equation x3+ax2+bx+c=0x^3+ax^2+bx+c=0, a,b,c∈Ra,b,c\in\mathbb{R}, then…MediumSingle correct
  7. 4 Apr 2026, Shift 2 · Q20The integral ∫01cot⁡−1(1+x+x2)dx\int_0^1\cot^{-1}\left(1+x+x^2\right)dx is equal to:HardSingle correct
  8. 5 Apr 2026, Shift 1 · Q18The value of the integral ∫0∞log⁡e(x)x2+4 dx\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx is:HardSingle correct
  9. 5 Apr 2026, Shift 1 · Q20The value of the integral ∫π/6π/3(4−cosec⁡2xcos⁡4x)dx\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx is:MediumSingle correct
  10. 5 Apr 2026, Shift 2 · Q18Let (21−a+21+a)(2^{1-a}+2^{1+a}), f(a)f(a), (3a+3−a)(3^a+3^{-a}) be in A.P. and α\alpha be the minimum value of f(a)f(a). Then the value of the integral…HardSingle correct
  11. 6 Apr 2026, Shift 1 · Q18The value of the integral ∫−π4π4(32cos⁡4x1+esin⁡x)dx\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx is:MediumSingle correct
  12. 6 Apr 2026, Shift 2 · Q20The value of the integral ∫−11(x3+∣x∣+1x2+2∣x∣+1)dx\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx is equal to :MediumSingle correct
  13. 8 Apr 2026, Shift 2 · Q16The value of the integral ∫02x (x2+x+1)(x+1)(x4+x2+1) dx\int_0^2 \frac{\sqrt{x}\,(x^2 + x + 1)}{(\sqrt{x} + 1)\left(\sqrt{x^4 + x^2 + 1}\right)}\,dx is equal to :HardSingle correct
  14. 8 Apr 2026, Shift 2 · Q22If…HardNumerical value

JEE Main 202513 questions

  1. 2 Apr 2025, Shift 1 · Q23Let [⋅][\cdot] denote the greatest integer function. If ∫0e3[1ex−1]dx=α−log⁡e2\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha-\log_e2, then α3\alpha^3 is…MediumNumerical value
  2. 2 Apr 2025, Shift 2 · Q184∫01(13+x2+1+x2)dx−3log⁡e(3)4\int_0^1 \left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right)\mathrm{d}x - 3\log_e(\sqrt{3}) is equal to :HardSingle correct
  3. 2 Apr 2025, Shift 2 · Q19Let (a,b)(a, b) be the point of intersection of the curve x2=2yx^2 = 2y and the straight line y−2x−6=0y - 2x - 6 = 0 in the second quadrant. Then the…MediumSingle correct
  4. 2 Apr 2025, Shift 2 · Q20Let f:[1,∞)→[2,∞)f : [1, \infty) \to [2, \infty) be a differentiable function. If 10∫1xf(t) dt=5xf(x)−x5−910\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9 for all…MediumSingle correct
  5. 3 Apr 2025, Shift 1 · Q18Let f(x)=∫x33−x2 dxf(x) = \int x^3\sqrt{3 - x^2}\,dx. If 5f(2)=−45f(\sqrt{2}) = -4, then f(1)f(1) is equal toMediumSingle correct
  6. 3 Apr 2025, Shift 1 · Q19Let the domain of the function f(x)=log⁡2log⁡4log⁡6(3+4x−x2)f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2) be (a,b)(a, b). If…HardSingle correct
  7. 3 Apr 2025, Shift 2 · Q18The integral ∫0π8x dx4cos⁡2x+sin⁡2x\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x} is equal toMediumSingle correct
  8. 4 Apr 2025, Shift 2 · Q18Let f(x)+2f(1x)=x2+5f(x)+2f\left(\frac{1}{x}\right)=x^2+5 and 2g(x)−3g(12)=x2g(x)-3g\left(\frac{1}{2}\right)=x, x>0x>0. If α=∫12f(x) dx\alpha=\int_1^2 f(x)\,dx, and…HardSingle correct
  9. 4 Apr 2025, Shift 2 · Q25If…HardNumerical value
  10. 7 Apr 2025, Shift 1 · Q18The integral ∫0π(x+3)sin⁡x1+3cos⁡2x dx\int_0^{\pi} \frac{(x+3)\sin x}{1+3\cos^2 x}\,dx is equal toMediumSingle correct
  11. 7 Apr 2025, Shift 2 · Q24If…HardNumerical value
  12. 8 Apr 2025, Shift 2 · Q18Let f(x)f(x) be a positive function and I1=∫−1212x f(2x(1−2x)) dxI_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx and…HardSingle correct
  13. 8 Apr 2025, Shift 2 · Q19The integral ∫−132(∣π2xsin⁡(πx)∣)dx\int_{-1}^{\frac{3}{2}} \left(\left|\pi^2 x \sin(\pi x)\right|\right) dx is equal to :MediumSingle correct

JEE Main 202440 questions

  1. 4 Apr 2024, Shift 1 · Q10Let f(x)={−2,−2≤x≤0x−2,0<x≤2f(x)=\begin{cases}-2, & -2 \le x \le 0\\ x-2, & 0<x \le 2\end{cases} and h(x)=f(∣x∣)+∣f(x)∣h(x)=f(|x|)+|f(x)|. Then ∫−22h(x) dx\int_{-2}^{2} h(x)\,dx is…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q25If ∫0π/4sin⁡2x1+sin⁡xcos⁡xdx=1alog⁡e(a3)+πb3\int_0^{\pi/4}\frac{\sin^2x}{1+\sin x\cos x}dx=\frac{1}{a}\log_e\left(\frac{a}{3}\right)+\frac{\pi}{b\sqrt{3}}, where…HardNumerical value
  3. 4 Apr 2024, Shift 2 · Q10If the value of the integral ∫−11cos⁡αx1+3xdx\int_{-1}^{1}\frac{\cos\alpha x}{1+3^x}dx is 2π\frac{2}{\pi}. Then, a value of α\alpha isMediumSingle correct
  4. 4 Apr 2024, Shift 2 · Q26If…HardNumerical value
  5. 5 Apr 2024, Shift 1 · Q10The value of ∫−ππ2y(1+sin⁡y)1+cos⁡2y dy\int_{-\pi}^{\pi}\frac{2y(1+\sin y)}{1+\cos^2 y}\,dy is :MediumSingle correct
  6. 5 Apr 2024, Shift 1 · Q11The integral ∫0π/4136sin⁡x3sin⁡x+5cos⁡x dx\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx is equal to :MediumSingle correct
  7. 5 Apr 2024, Shift 2 · Q11Let β(m,n)=∫01xm−1(1−x)n−1 dx\beta(m, n) = \int_0^1 x^{m-1}(1-x)^{n-1}\,dx, m,n>0m, n > 0. If ∫01(1−x10)20 dx=a×β(b,c)\int_0^1 (1-x^{10})^{20}\,dx = a \times \beta(b, c), then…MediumSingle correct
  8. 5 Apr 2024, Shift 2 · Q25If f(t)=∫0π2x dx1−cos⁡2tsin⁡2xf(t) = \int_0^{\pi} \frac{2x\,dx}{1-\cos^2 t \sin^2 x}, 0<t<π0 < t < \pi, then the value of…HardNumerical value
  9. 6 Apr 2024, Shift 1 · Q11∫0π/4cos⁡2x sin⁡2x(cos⁡3x+sin⁡3x)2dx\int_0^{\pi/4}\frac{\cos^2 x\ \sin^2 x}{(\cos^3 x+\sin^3 x)^2}dx is equal toMediumSingle correct
  10. 6 Apr 2024, Shift 1 · Q25Let rk=∫01(1−x7)kdx∫01(1−x7)k+1dxr_k=\frac{\int_0^1\left(1-x^7\right)^k dx}{\int_0^1\left(1-x^7\right)^{k+1}dx}, k∈Nk \in \mathbb{N}. Then the value of…HardNumerical value
  11. 6 Apr 2024, Shift 2 · Q12If ∫1a2sin⁡2x+b2cos⁡2xdx=112tan⁡−1(3tan⁡x)+constant\int\frac{1}{a^2\sin^2x+b^2\cos^2x}dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}, then the maximum value of asin⁡x+bcos⁡xa\sin x+b\cos x, is :MediumSingle correct
  12. 6 Apr 2024, Shift 2 · Q25Let [t][t] denote the largest integer less than or equal to tt. If…HardNumerical value
  13. 8 Apr 2024, Shift 1 · Q10Let I(x)=∫6sin⁡2x(1−cot⁡x)2dxI(x)=\int\frac{6}{\sin^2x(1-\cot x)^2}dx. If I(0)=3I(0)=3, then I(π12)I\left(\frac{\pi}{12}\right) is equal toMediumSingle correct
  14. 8 Apr 2024, Shift 1 · Q11Reduction Formulae in Definite Integrals · Hard · Single correct
  15. 8 Apr 2024, Shift 2 · Q11Exponential Factor Manipulation · Hard · Single correct
  16. 8 Apr 2024, Shift 2 · Q26Fractional Powers LCM Substitution · Hard · Numerical value
  17. 9 Apr 2024, Shift 1 · Q8Numerator-Denominator Derivative Matching · Medium · Single correct
  18. 9 Apr 2024, Shift 1 · Q28Summation to Riemann Form · Hard · Numerical value
  19. 9 Apr 2024, Shift 2 · Q9Limit Evaluation · Hard · Single correct
  20. 9 Apr 2024, Shift 2 · Q11Multiple Angle Inverse ID · Medium · Single correct
  21. 9 Apr 2024, Shift 2 · Q12Logarithm of Quadratic Roots · Medium · Single correct
  22. 1 Feb 2024, Shift 1 · Q10King's Property · Hard · Single correct
  23. 1 Feb 2024, Shift 1 · Q27Symmetric Limits with Exponential Denominator Trick · Hard · Numerical value
  24. 1 Feb 2024, Shift 2 · Q10Reduction Formulae in Definite Integrals · Medium · Single correct
  25. 1 Feb 2024, Shift 2 · Q11King's Property · Medium · Single correct
  26. 1 Feb 2024, Shift 2 · Q24Solving Integral Equations · Medium · Numerical value
  27. 27 Jan 2024, Shift 1 · Q11Open the question · Medium · Single correct
  28. 27 Jan 2024, Shift 1 · Q12King's Property · Hard · Single correct
  29. 29 Jan 2024, Shift 1 · Q11Symmetric Limits with Exponential Denominator Trick · Hard · Single correct
  30. 29 Jan 2024, Shift 1 · Q12Odd Power of Cosine Substitution · Hard · Single correct
  31. 30 Jan 2024, Shift 1 · Q8L'Hopital with Leibniz Rule · Medium · Single correct
  32. 30 Jan 2024, Shift 1 · Q10Summation to Riemann Form · Medium · Single correct
  33. 30 Jan 2024, Shift 1 · Q25Greatest Integer Function Integrals · Hard · Numerical value
  34. 30 Jan 2024, Shift 2 · Q10Open the question · Medium · Single correct
  35. 30 Jan 2024, Shift 2 · Q12Composite Function Substitution · Hard · Single correct
  36. 30 Jan 2024, Shift 2 · Q13Composite Function Substitution · Hard · Single correct
  37. 31 Jan 2024, Shift 1 · Q26King's Property · Hard · Numerical value
  38. 31 Jan 2024, Shift 1 · Q27Fractional Powers LCM Substitution · Hard · Numerical value
  39. 31 Jan 2024, Shift 2 · Q12Even and Odd Functions · Hard · Single correct
  40. 31 Jan 2024, Shift 2 · Q26Removing 'x' using King's Property · Hard · Numerical value

JEE Main 202322 questions

  1. 6 Apr 2023, Shift 1 · Q10Open the question · Medium · Single correct
  2. 6 Apr 2023, Shift 1 · Q11Generalized Reverse Product Rule · Hard · Single correct
  3. 6 Apr 2023, Shift 2 · Q11King's Property · Medium · Single correct
  4. 6 Apr 2023, Shift 2 · Q26Open the question · Hard · Numerical value
  5. 8 Apr 2023, Shift 1 · Q11Implicit Derivative Recognition · Hard · Single correct
  6. 8 Apr 2023, Shift 1 · Q24Greatest Integer Function Integrals · Hard · Numerical value
  7. 8 Apr 2023, Shift 2 · Q26Greatest Integer Function Integrals · Medium · Numerical value
  8. 10 Apr 2023, Shift 1 · Q8Trigonometric Substitution · Hard · Single correct
  9. 10 Apr 2023, Shift 2 · Q10Exponential Factor Manipulation · Hard · Single correct
  10. 10 Apr 2023, Shift 2 · Q11Solving Integral Equations · Medium · Single correct
  11. 11 Apr 2023, Shift 1 · Q15Logarithm of Quadratic Roots · Hard · Single correct
  12. 11 Apr 2023, Shift 1 · Q26Algebraic Reduction Formulas · Hard · Numerical value
  13. 11 Apr 2023, Shift 2 · Q11Greatest Integer Function Integrals · Hard · Single correct
  14. 11 Apr 2023, Shift 2 · Q12Open the question · Hard · Single correct
  15. 12 Apr 2023, Shift 1 · Q26Interval Splitting · Medium · Numerical value
  16. 12 Apr 2023, Shift 1 · Q27Fractional Powers LCM Substitution · Hard · Numerical value
  17. 13 Apr 2023, Shift 1 · Q11Algebraic Manipulation · Medium · Single correct
  18. 13 Apr 2023, Shift 1 · Q25Open the question · Hard · Numerical value
  19. 13 Apr 2023, Shift 2 · Q10Reduction Formulae in Definite Integrals · Hard · Single correct
  20. 13 Apr 2023, Shift 2 · Q26Odd Power of Cosine Substitution · Hard · Numerical value
  21. 15 Apr 2023, Shift 1 · Q10King's Property · Hard · Single correct
  22. 15 Apr 2023, Shift 1 · Q26Algebraic Manipulation · Hard · Numerical value

JEE Main 202245 questions

  1. 25 Jul 2022, Shift 1 · Q9Periodic Function Property · Hard · Single correct
  2. 25 Jul 2022, Shift 1 · Q27Summation to Riemann Form · Medium · Numerical value
  3. 25 Jul 2022, Shift 2 · Q7Summation to Riemann Form · Medium · Single correct
  4. 25 Jul 2022, Shift 2 · Q9Greatest Integer Function Integrals · Medium · Single correct
  5. 25 Jul 2022, Shift 2 · Q26Solving Integral Equations · Hard · Numerical value
  6. 25 Jul 2022, Shift 2 · Q27Open the question · Hard · Numerical value
  7. 26 Jul 2022, Shift 1 · Q10Summation to Riemann Form · Medium · Single correct
  8. 26 Jul 2022, Shift 1 · Q26Open the question · Hard · Numerical value
  9. 26 Jul 2022, Shift 2 · Q9Periodic Function Property · Medium · Single correct
  10. 26 Jul 2022, Shift 2 · Q19Twin Trigonometric Integrals Substitution · Hard · Single correct
  11. 27 Jul 2022, Shift 1 · Q7Greatest Integer Function Integrals · Medium · Single correct
  12. 27 Jul 2022, Shift 1 · Q8Bounding and Estimation Property · Medium · Single correct
  13. 27 Jul 2022, Shift 2 · Q9Greatest Integer Function Integrals · Medium · Single correct
  14. 27 Jul 2022, Shift 2 · Q27Greatest Integer Function Integrals · Hard · Numerical value
  15. 28 Jul 2022, Shift 1 · Q24Pure Quadratic Outside and Inside Root Substitution · Hard · Numerical value
  16. 28 Jul 2022, Shift 2 · Q69Algebraic Reduction Formulas · Hard · Single correct
  17. 28 Jul 2022, Shift 2 · Q90Open the question · Medium · Numerical value
  18. 29 Jul 2022, Shift 1 · Q6Weierstrass Substitution · Hard · Single correct
  19. 29 Jul 2022, Shift 1 · Q15Reciprocal Limits Substitution Trick · Hard · Single correct
  20. 29 Jul 2022, Shift 2 · Q5Greatest Integer Function Integrals · Hard · Single correct
  21. 29 Jul 2022, Shift 2 · Q8Open the question · Hard · Single correct
  22. 30 Jul 2022, Shift 2 · Q71Periodic Function Property · Hard · Single correct
  23. 30 Jul 2022, Shift 2 · Q72Algebraic Manipulation to Extract 1/n · Hard · Single correct
  24. 24 Jun 2022, Shift 1 · Q26Open the question · Hard · Numerical value
  25. 24 Jun 2022, Shift 1 · Q27Max/Min Function Integrals · Hard · Numerical value
  26. 24 Jun 2022, Shift 2 · Q6Symmetric Limits with Exponential Denominator Trick · Medium · Single correct
  27. 24 Jun 2022, Shift 2 · Q7Summation to Riemann Form · Hard · Single correct
  28. 25 Jun 2022, Shift 1 · Q2Symmetric Limits with Exponential Denominator Trick · Medium · Single correct
  29. 25 Jun 2022, Shift 2 · Q12Reduction Formulae in Definite Integrals · Hard · Single correct
  30. 25 Jun 2022, Shift 2 · Q23Open the question · Medium · Numerical value
  31. 26 Jun 2022, Shift 1 · Q24Integrals of Min and Max Functions · Medium · Numerical value
  32. 26 Jun 2022, Shift 1 · Q28King's Property · Hard · Numerical value
  33. 26 Jun 2022, Shift 2 · Q8Cosine Double Angle Radical Substitution · Hard · Single correct
  34. 26 Jun 2022, Shift 2 · Q28Factoring Highest Power for Substitution · Hard · Numerical value
  35. 27 Jun 2022, Shift 1 · Q9Exponential Form with Improper Rational Functions · Medium · Single correct
  36. 27 Jun 2022, Shift 1 · Q10Symmetric Limits with Exponential Denominator Trick · Medium · Single correct
  37. 27 Jun 2022, Shift 2 · Q8Variable Limit Leibniz · Medium · Single correct
  38. 27 Jun 2022, Shift 2 · Q9Greatest Integer Function Integrals · Hard · Single correct
  39. 28 Jun 2022, Shift 1 · Q7Greatest Integer Function Integrals · Hard · Single correct
  40. 28 Jun 2022, Shift 2 · Q7Open the question · Hard · Single correct
  41. 28 Jun 2022, Shift 2 · Q8Periodic Function Property · Hard · Single correct
  42. 29 Jun 2022, Shift 1 · Q17Greatest Integer Function Integrals · Medium · Single correct
  43. 29 Jun 2022, Shift 2 · Q7Solving Integral Equations · Medium · Single correct
  44. 30 Jun 2022, Shift 1 · Q11Summation to Riemann Form · Medium · Single correct
  45. 30 Jun 2022, Shift 1 · Q25Variable Limit Leibniz · Hard · Numerical value

JEE Main 202154 questions

  1. 3 Aug 2021, Shift 1 · Q69General Linear Outside, Quadratic Inside Root Substitution · Medium · Single correct
  2. 3 Aug 2021, Shift 1 · Q70Greatest Integer Function Integrals · Medium · Single correct
  3. 3 Aug 2021, Shift 2 · Q72Open the question · Medium · Single correct
  4. 3 Aug 2021, Shift 2 · Q84Greatest Integer Function Integrals · Medium · Numerical value
  5. 4 Aug 2021, Shift 1 · Q69King's Property · Medium · Single correct
  6. 4 Aug 2021, Shift 1 · Q86Twin Trigonometric Integrals Substitution · Hard · Numerical value
  7. 4 Aug 2021, Shift 2 · Q69Inverse Trig Simplification Before Parts · Medium · Single correct
  8. 4 Aug 2021, Shift 2 · Q70King's Property · Medium · Single correct
  9. 4 Aug 2021, Shift 2 · Q71Fractional Part Function Integrals · Medium · Single correct
  10. 4 Aug 2021, Shift 2 · Q88Square Root Derivative Integration Rule · Easy · Numerical value
  11. 26 Aug 2021, Shift 1 · Q69Modulus Function Interval Splitting · Hard · Single correct
  12. 26 Aug 2021, Shift 1 · Q70Fractional or Multiple Upper Bounds · Medium · Single correct
  13. 26 Aug 2021, Shift 2 · Q67Symmetric Limits with Exponential Denominator Trick · Medium · Single correct
  14. 26 Aug 2021, Shift 2 · Q74Greatest Integer Function Integrals · Medium · Single correct
  15. 27 Aug 2021, Shift 1 · Q68Product Series with Variable Exponents · Hard · Single correct
  16. 27 Aug 2021, Shift 1 · Q77King's Property · Medium · Single correct
  17. 27 Aug 2021, Shift 1 · Q90Tangent Trigonometric Substitution · Hard · Numerical value
  18. 27 Aug 2021, Shift 2 · Q70Fractional Powers LCM Substitution · Hard · Single correct
  19. 27 Aug 2021, Shift 2 · Q84Numerator-Denominator Derivative Matching · Medium · Numerical value
  20. 31 Aug 2021, Shift 1 · Q70Rational Powers Summing to Two Substitution · Medium · Single correct
  21. 31 Aug 2021, Shift 1 · Q72Constant Limit Leibniz · Hard · Single correct
  22. 31 Aug 2021, Shift 1 · Q84Greatest Integer Function Integrals · Medium · Numerical value
  23. 31 Aug 2021, Shift 2 · Q69Greatest Integer Function Integrals · Hard · Single correct
  24. 31 Aug 2021, Shift 2 · Q86Negative Even Sum of Trig Powers Substitution · Hard · Numerical value
  25. 24 Feb 2021, Shift 1 · Q66Limit Evaluation · Medium · Single correct
  26. 24 Feb 2021, Shift 1 · Q70sin(2x) Derivative Substitution · Medium · Single correct
  27. 24 Feb 2021, Shift 1 · Q87Greatest Integer Function Integrals · Medium · Numerical value
  28. 24 Feb 2021, Shift 2 · Q65Greatest Integer Function Integrals · Medium · Single correct
  29. 24 Feb 2021, Shift 2 · Q68King's Property · Medium · Single correct
  30. 25 Feb 2021, Shift 1 · Q67Composite Function Substitution · Hard · Single correct
  31. 25 Feb 2021, Shift 1 · Q68Greatest Integer Function Integrals · Medium · Single correct
  32. 25 Feb 2021, Shift 2 · Q64Reduction Formulae in Definite Integrals · Hard · Single correct
  33. 25 Feb 2021, Shift 2 · Q68Logarithmic Derivative Integration Rule · Medium · Single correct
  34. 25 Feb 2021, Shift 2 · Q74Summation to Riemann Form · Medium · Single correct
  35. 25 Feb 2021, Shift 2 · Q86Modulus Function Interval Splitting · Medium · Numerical value
  36. 26 Feb 2021, Shift 1 · Q69Symmetric Limits with Exponential Denominator Trick · Medium · Single correct
  37. 26 Feb 2021, Shift 1 · Q80Fractional Part Function Integrals · Easy · Single correct
  38. 26 Feb 2021, Shift 1 · Q88Modulus Function Interval Splitting · Easy · Numerical value
  39. 26 Feb 2021, Shift 2 · Q80Reciprocal Substitution (x = 1/t) · Medium · Single correct
  40. 26 Feb 2021, Shift 2 · Q81Beta Function Integrals · Hard · Numerical value
  41. 22 Jul 2021, Shift 2 · Q76Periodic Function Property · Hard · Single correct
  42. 25 Jul 2021, Shift 1 · Q78King's Property Rational Shortcut · Medium · Single correct
  43. 25 Jul 2021, Shift 2 · Q69Even and Odd Functions · Easy · Single correct
  44. 16 Mar 2021, Shift 2 · Q72Open the question · Easy · Single correct
  45. 16 Mar 2021, Shift 2 · Q74Greatest Integer Function Integrals · Medium · Single correct
  46. 16 Mar 2021, Shift 2 · Q81Composite Function Substitution · Hard · Numerical value
  47. 17 Mar 2021, Shift 1 · Q85Greatest Integer Function Integrals · Hard · Numerical value
  48. 17 Mar 2021, Shift 2 · Q66Greatest Integer Function Integrals · Hard · Single correct
  49. 17 Mar 2021, Shift 2 · Q75Bounding and Estimation Property · Medium · Single correct
  50. 17 Mar 2021, Shift 2 · Q81Algebraic Reduction Formulas · Medium · Numerical value
  51. 18 Mar 2021, Shift 1 · Q73Composite Function Substitution · Medium · Single correct
  52. 18 Mar 2021, Shift 1 · Q82Even and Odd Functions · Hard · Numerical value
  53. 18 Mar 2021, Shift 1 · Q83Quotient Rule Differential Recognition · Hard · Numerical value
  54. 18 Mar 2021, Shift 2 · Q71Bounding and Estimation Property · Medium · Single correct

JEE Main 202021 questions

  1. 8 Jan 2020, Shift 1 · Q60Factoring Highest Power for Substitution · Hard · Single correct
  2. 8 Jan 2020, Shift 2 · Q58L'Hopital with Leibniz Rule · Easy · Single correct
  3. 8 Jan 2020, Shift 2 · Q61Bounding and Estimation Property · Hard · Single correct
  4. 9 Jan 2020, Shift 1 · Q51Open the question · Medium · Single correct
  5. 9 Jan 2020, Shift 1 · Q61Periodic Reduction of tan-1(tan x) and cot-1(cot x) · Hard · Single correct
  6. 9 Jan 2020, Shift 1 · Q62Rational Powers Summing to Two Substitution · Medium · Single correct
  7. 9 Jan 2020, Shift 1 · Q63King's Property · Medium · Single correct
  8. 9 Jan 2020, Shift 2 · Q62Even Power of Secant Substitution · Medium · Single correct
  9. 2 Sep 2020, Shift 1 · Q73Modulus Function Interval Splitting · Easy · Numerical value
  10. 2 Sep 2020, Shift 2 · Q74Greatest Integer Function Integrals · Medium · Numerical value
  11. 3 Sep 2020, Shift 1 · Q60Modulus Function Interval Splitting · Easy · Single correct
  12. 3 Sep 2020, Shift 2 · Q60Inverse Trig Simplification Before Parts · Hard · Single correct
  13. 3 Sep 2020, Shift 2 · Q61Trigonometric Substitution · Medium · Single correct
  14. 4 Sep 2020, Shift 1 · Q60Geometric Area for Piecewise Linear Integrals · Medium · Single correct
  15. 4 Sep 2020, Shift 1 · Q61Integrability over ILATE · Hard · Single correct
  16. 4 Sep 2020, Shift 1 · Q62Fractional Powers LCM Substitution · Medium · Single correct
  17. 4 Sep 2020, Shift 2 · Q61Implicit Derivative Recognition · Hard · Single correct
  18. 4 Sep 2020, Shift 2 · Q73Fractional Part Function Integrals · Medium · Numerical value
  19. 5 Sep 2020, Shift 1 · Q61Exponential Special Form · Hard · Single correct
  20. 5 Sep 2020, Shift 1 · Q62King's Property · Easy · Single correct
  21. 6 Sep 2020, Shift 2 · Q61Exact Exponential-Function Derivative Substitution · Hard · Single correct

JEE Main 20172 questions

  1. 2 Apr 2017 (offline) · Q74Trigonometric Reduction Formulas · Medium · Single correct
  2. 2 Apr 2017 (offline) · Q75Weierstrass Substitution · Easy · 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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