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Saturday, 31 October

JEE Main · Maths · Binomial Theorem

Second Derivative Method for Sums

JEE Main asked Second Derivative Method for Sums 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2024 and 2025. It belongs to Binomial Coefficients, in Binomial Theorem (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 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.

  • Evaluate sum of r^2 times binomial coefficients
  • N from binomial sum inequality

Difficulty

Easy 0Medium 2Hard 1

1 of the 3 questions had a numerical answer.

Every question

All 3 questions

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

  1. 4 Apr 2025, Shift 2 · Q7If 12⋅(15C1)+22⋅(15C2)+32⋅(15C3)+…+152⋅(15C15)=2m⋅3n⋅5k1^2\cdot({}^{15}C_1)+2^2\cdot({}^{15}C_2)+3^2\cdot({}^{15}C_3)+\ldots+15^2\cdot({}^{15}C_{15})=2^m\cdot3^n\cdot5^k, where…MediumSingle correct
  2. 8 Apr 2024, Shift 1 · Q24Let α=∑r=0n(4r2+2r+1) nCr\alpha=\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r and β=(∑r=0nnCrr+1)+1n+1\beta=\left(\sum_{r=0}^{n}\frac{{}^nC_r}{r+1}\right)+\frac{1}{n+1}. If…HardNumerical value
  3. 26 Aug 2021, Shift 1 · Q66If 20Cr^{20}C_r is the co-efficient of xrx^r in the expansion of (1+x)20(1+x)^{20}, then the value of ∑r=020r2 20Cr\sum_{r=0}^{20} r^2\,{}^{20}C_r is equal…MediumSingle correct

Shifts: 26 Aug 2021, Shift 1, 8 Apr 2024, Shift 1, 4 Apr 2025, Shift 2.

Same topic

Other ideas in Binomial Coefficients

Binomial Coefficients has 28 ideas JEE Main has asked; 15 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas