JEE Main · Maths · Vector Algebra

Cross Product: JEE Main previous year questions

Name: Cross Product: JEE Main previous year questions
Creator: Lumi

72 questions in the 108 JEE Main shifts Lumi analysed, in 8 of 8 years. Pattern: Asked most years. 32 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 72; in 61 of 108 shifts
Years asked: 8/8; last asked 2026
Chance in a shift: 47%; calibrated model, how we compute it
Weighted estimate: 0.7; model; history: 0.6 a shift on average, typically 0.4–0.9

Key findings

01
Asked in 8 of 8 years with analysed shifts and in 61 of 108 shifts: 72 questions, #26 of 196 topics. It came in every year with analysed shifts.
02
17% of its questions since 2020 tested an idea no earlier year had asked; 52 repeated an idea from the year before.
03
The most repeated idea is Solving Vector Equations with Cross Products, asked 20 times in 20 shifts (2020, 2021, 2022, 2023, 2024, 2026), most often as “unknown vector from cross and dot conditions”.
04
JEE Main has asked 13 of the 64 ideas in this topic; 45 have never been asked, directly or inside another question.
05
Mostly asked as single correct (64%); 33% need a numerical answer, 6% are easy and 32% hard.
06
The skill tested most is multi-step (74%), then calculation (25%).

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.

Raw count: 2017: 1 in 1 shift · 2020: 3 in 12 shifts · 2021: 12 in 24 shifts · 2022: 12 in 24 shifts · 2023: 12 in 12 shifts · 2024: 22 in 18 shifts · 2025: 5 in 8 shifts · 2026: 5 in 9 shifts.

Up to 2023: 0.6; a shift, of 25
Since 2024: 0.7; 0.2
Usual gap: 1.3 yrs; between years asking it
Shifts with it: 61/108; 56% of analysed shifts

Recent framings

unknown vector from cross and dot conditions
numerical: solve vector cross product equation
numerical: area of triangle from vector combinations

Revise first

Solving Vector Equations with Cross Products · asked 2020, 2021, 2022, 2023, 2024, 2026
Magnitude and Sine Formula · asked 2017, 2020, 2021, 2022, 2023, 2024, 2026
Area of Triangles and Parallelograms · asked 2021, 2022, 2023, 2024, 2025, 2026

How it is asked

Difficulty, format and skill

Across all 72 questions on Cross Product since 2017.

Difficulty

QUESTIONS

4523

Easy4 · 6%
Medium45 · 63%
Hard23 · 32%

Format

Single correct · 46 Q64%
Numerical value · 24 Q33%
Two statements · 2 Q3%

Skill tested

Multi-step · 53 Q74%
Calculation · 18 Q25%
Application · 1 Q1%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 13 of the 64 ideas in this topic. 45 have never been asked yet.

13645

Asked directly13 · 20%
Touched inside another question6 · 9%
Never asked45 · 70%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Chapter, idea, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

chapterAskedShareYears’17’20’21’22’23’24’25’26

Open71 · 99%99%8/831212122245
13 ideas inside
- OpenRepeated20 · 28%28%6/843273
- OpenRepeated13 · 18%18%7/82323
- OpenRepeated8 · 11%11%5/832
- OpenRepeated7 · 10%10%3/85
- OpenRepeated7 · 10%10%5/822
- OpenRepeated6 · 8%8%5/82
- OpenRepeated2 · 3%3%2/8
- OpenRepeated2 · 3%3%2/8
- OpenRepeated2 · 3%3%2/8
- Open1 · 1%1%1/8
- Open1 · 1%1%1/8
- Open1 · 1%1%1/8
- Open1 · 1%1%1/8
Open1 · 1%1%1/8

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

Every idea inside this topic

13 different ideas were tested; 9 came more than once.

Solving Vector Equations with Cross Products20×
unknown vector from cross and dot conditions
Single correct · 20 shifts · 6 numerical
Magnitude and Sine Formula13×
unknown vector from cross and dot conditions
Single correct · 13 shifts · 3 numerical
Lagrange's Identity8×
unknown vector from cross and dot conditions
Numerical value · 7 shifts · 4 numerical
Area of Triangles and Parallelograms7×
area of triangle from vector combinations
Single correct · 7 shifts · 2 numerical
Simultaneous Cross and Dot Equations7×
unknown vector from cross and dot conditions
Numerical value · 7 shifts · 5 numerical
Area of Quadrilateral via Diagonals7×
area of quadrilateral from vertices
Single correct · 7 shifts
Condition for Parallel Vectors2×
vector from cross product condition
Numerical value · 2 shifts · 1 numerical
Determinant Calculation Method2×
unknown components from cross product
Numerical value · 2 shifts · 1 numerical
Unit Normal Vector Calculation2×
vector perpendicular to two given
Numerical value · 2 shifts · 1 numerical
Orthogonality Dot Product Trap1×
dot products of vector with cross-product combination
Single correct · 1 shift
General Solution of a x x = b1×
unknown vector from cross and dot conditions
Numerical value · 1 shift · 1 numerical
Anti-commutativity and Distributivity1×
magnitude of cross product of combinations
Single correct · 1 shift
Orthogonal Triad Expansion1×
find false statement from cyclic cross product relations
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Solving Vector Equations with Cross Productsunknown vector from cross and dot conditions	20	20	Single correctMulti-step	6
Magnitude and Sine Formulaunknown vector from cross and dot conditions	13	13	Single correctMulti-step	3
Lagrange's Identityunknown vector from cross and dot conditions	8	7	Numerical valueCalculation	4
Area of Triangles and Parallelogramsarea of triangle from vector combinations	7	7	Single correctMulti-step	2
Simultaneous Cross and Dot Equationsunknown vector from cross and dot conditions	7	7	Numerical valueMulti-step	5
Area of Quadrilateral via Diagonalsarea of quadrilateral from vertices	7	7	Single correctCalculation	–
Condition for Parallel Vectorsvector from cross product condition	2	2	Numerical valueMulti-step	1
Determinant Calculation Methodunknown components from cross product	2	2	Numerical valueCalculation	1
Unit Normal Vector Calculationvector perpendicular to two given	2	2	Numerical valueCalculation	1
Orthogonality Dot Product Trapdot products of vector with cross-product combination	1	1	Single correctCalculation	–
General Solution of a x x = bunknown vector from cross and dot conditions	1	1	Numerical valueMulti-step	1
Anti-commutativity and Distributivitymagnitude of cross product of combinations	1	1	Single correctCalculation	–
Orthogonal Triad Expansionfind false statement from cyclic cross product relations	1	1	Single correctMulti-step	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Cross Product questions, year by year

The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Chapter, idea, question

Every idea inside this topic

Cross Product questions, year by year

JEE Main 20265 questions in 5 shifts

JEE Main 20255 questions in 5 shifts

JEE Main 202422 questions in 15 shifts

JEE Main 202312 questions in 10 shifts

JEE Main 202212 questions in 10 shifts

JEE Main 202112 questions in 12 shifts

JEE Main 20203 questions in 3 shifts

JEE Main 20171 question in 1 shift

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