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Saturday, 31 October

JEE Main · Maths · Integrals

Summation to Riemann Form

JEE Main asked Summation to Riemann Form 9 times in 9 of the 108 shifts Lumi analysed, in 2021, 2022, 2023 and 2024. It belongs to Integral as Limit of Sum, in Integrals (Maths). The longest wait between two years asking it was 1 year. In 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
9
in 9 shifts
Years
4 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.18’220.07’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 5 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20242 of 18
  • 20231 of 12
  • 20225 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Limit of sum as definite integral
  • Limit of a sum as definite integral

Difficulty

Easy 0Medium 7Hard 2

2 of the 9 questions had a numerical answer.

Every question

All 9 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 30 Jan 2024, Shift 1 · Q10The value of lim⁡n→∞∑k=1nn3(n2+k2)(n2+3k2)\lim_{n\to\infty}\sum_{k=1}^{n}\frac{n^3}{(n^2+k^2)(n^2+3k^2)} is :MediumSingle correct
  2. 9 Apr 2024, Shift 1 · Q28Let…HardNumerical value
  3. 13 Apr 2023, Shift 1 · Q7Among (S1) : lim⁡n→∞1n2(2+4+6+……+2n)=1\lim_{n\to\infty}\frac{1}{n^2}(2+4+6+\ldots\ldots+2n)=1 (S2) :…MediumTwo statements
  4. 30 Jun 2022, Shift 1 · Q11lim⁡n→∞∑r=1nr2r2−7rn+6n2\lim_{n\to\infty} \sum_{r=1}^{n} \frac{r}{2r^2 - 7rn + 6n^2} is equal to :MediumSingle correct
  5. 24 Jun 2022, Shift 2 · Q7…HardSingle correct
  6. 26 Jul 2022, Shift 1 · Q10If a=lim⁡n→∞∑k=1n2nn2+k2\mathrm{a} = \lim_{n \to \infty} \sum_{k=1}^{n} \dfrac{2n}{n^2 + k^2} and f(x)=1−cos⁡x1+cos⁡xf(x) = \sqrt{\dfrac{1 - \cos x}{1 + \cos x}},…MediumSingle correct
  7. 25 Jul 2022, Shift 2 · Q7…MediumSingle correct
  8. 25 Jul 2022, Shift 1 · Q27If…MediumNumerical value
  9. 25 Feb 2021, Shift 2 · Q74lim⁡n→∞[1n+n(n+1)2+n(n+2)2+………+n(2n−1)2]\lim_{n\to\infty}\left[\frac{1}{n} + \frac{n}{(n+1)^2} + \frac{n}{(n+2)^2} + \ldots\ldots\ldots + \frac{n}{(2n-1)^2}\right] is equal to :MediumSingle correct

Shifts: 25 Feb 2021, Shift 2, 24 Jun 2022, Shift 2, 30 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 25 Jul 2022, Shift 1, 26 Jul 2022, Shift 1, 13 Apr 2023, Shift 1, 30 Jan 2024, Shift 1, 9 Apr 2024, Shift 1.

Same topic

Other ideas in Integral as Limit of Sum

Integral as Limit of Sum has 5 ideas JEE Main has asked; 1 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas