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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Expansion of Sum of Vectors Squared

JEE Main asked Expansion of Sum of Vectors Squared 4 times in 4 of the 108 shifts Lumi analysed, in 2020, 2021, 2024 and 2025. It belongs to Dot Product, in Vector Algebra (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
4 of 8
First asked
2020
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.03’210’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 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
  • 20201 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.

  • Value from ratio of sum and difference magnitudes
  • Magnitude of vector expression from cross product

Difficulty

Easy 2Medium 2Hard 0

1 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 7 Apr 2025, Shift 2 · Q15Let a⃗\vec{a} and b⃗\vec{b} be the vectors of the same magnitude such that…MediumSingle correct
  2. 30 Jan 2024, Shift 2 · Q18Let a⃗\vec{a} and b⃗\vec{b} be two vectors such that ∣b⃗∣=1|\vec{b}| = 1 and ∣b⃗×a⃗∣=2|\vec{b} \times \vec{a}| = 2. Then…EasySingle correct
  3. 31 Aug 2021, Shift 1 · Q78Let a⃗\vec{\mathrm{a}} and b⃗\vec{\mathrm{b}} be two vectors such that…MediumSingle correct
  4. 6 Sep 2020, Shift 2 · Q74If x⃗\vec{x} and y⃗\vec{y} be two non-zero vectors such that ∣x⃗+y⃗∣=∣x⃗∣|\vec{x}+\vec{y}|=|\vec{x}| and 2x⃗+λy⃗2\vec{x}+\lambda\vec{y} is perpendicular…EasyNumerical value

Shifts: 6 Sep 2020, Shift 2, 31 Aug 2021, Shift 1, 30 Jan 2024, Shift 2, 7 Apr 2025, Shift 2.

Same topic

Other ideas in Dot Product

Dot Product has 16 ideas JEE Main has asked; 4 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas