JEE Main · Maths · Vector Algebra

Linear Independence: JEE Main previous year questions

Name: Linear Independence: JEE Main previous year questions
Creator: Lumi

6 questions in the 108 JEE Main shifts Lumi analysed, in 4 of 8 years. Pattern: Comes in cycles. 1 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 6; in 6 of 108 shifts
Years asked: 4/8; last asked 2024
Chance in a shift: 9%; calibrated model, how we compute it
Weighted estimate: 0.0; model; history: 0.0 a shift on average, typically 0.0–0.1

Key findings

01
Asked in 4 of 8 years with analysed shifts and in 6 of 108 shifts: 6 questions, #188 of 196 topics. Last asked in 2024.
02
83% of its questions since 2020 tested an idea no earlier year had asked; 1 repeated an idea from the year before.
03
The most repeated idea is Collinearity of Three Position Vectors, asked 2 times in 2 shifts (2022, 2023), most often as “unknowns from collinearity of three points”.
04
JEE Main has asked 5 of the 63 ideas in this topic; 55 have never been asked, directly or inside another question.
05
Mostly asked as single correct (100%); 0% need a numerical answer, 50% are easy and 0% hard.
06
The skill tested most is multi-step (33%), then calculation (33%).

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

Up to 2023: 0.1; a shift, of 25
Since 2024: 0.0; 0.0
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 6/108; 6% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 6 questions on Linear Independence since 2017.

Difficulty

QUESTIONS

Easy3 · 50%
Medium3 · 50%
Hard0 · 0%

Format

Single correct · 6 Q100%

Skill tested

Multi-step · 2 Q33%
Calculation · 2 Q33%
Application · 2 Q33%

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 5 of the 63 ideas in this topic. 55 have never been asked yet.

Asked directly5 · 8%
Touched inside another question3 · 5%
Never asked55 · 87%

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

Idea, year, question

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

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

OpenRepeated2 · 33%33%2/8
- 8 Apr ’23 S1 · Q17
  If the points with position vectors $\alpha\hat{i}+10\hat{j}+13\hat{k}$ , $6\hat{i}+11\hat{j}+11\hat{k}$ ,…
  mediumSingle correctAsked the year before
- 29 Jun ’22 S2 · Q15
  Let $A, B, C$ be three points whose position vectors respectively are $\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}$ …
  easySingle correctNew idea
Open1 · 17%17%1/8
Open1 · 17%17%1/8
Open1 · 17%17%1/8
Open1 · 17%17%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

5 different ideas were tested; 1 came more than once.

Collinearity of Three Position Vectors2×
unknowns from collinearity of three points
Single correct · 2 shifts
Linear Combination Concept1×
coefficients from collinearity of vector combinations
Single correct · 1 shift
Unique Linear Combinations1×
express vector in terms of two vectors
Single correct · 1 shift
Independence of Three Vectors1×
parameter set for independent vectors
Single correct · 1 shift
Proportionality Test for Collinearity1×
unit vector from collinearity of two vectors
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Collinearity of Three Position Vectorsunknowns from collinearity of three points	2	2	Single correctApplication	–
Linear Combination Conceptcoefficients from collinearity of vector combinations	1	1	Single correctMulti-step	–
Unique Linear Combinationsexpress vector in terms of two vectors	1	1	Single correctMulti-step	–
Independence of Three Vectorsparameter set for independent vectors	1	1	Single correctCalculation	–
Proportionality Test for Collinearityunit vector from collinearity of two vectors	1	1	Single correctApplication	–

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

Linear Independence questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it 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

Idea, year, question

Every idea inside this topic

Linear Independence questions, year by year

JEE Main 20241 question in 1 shift

JEE Main 20232 questions in 2 shifts

JEE Main 20222 questions in 2 shifts

JEE Main 20211 question in 1 shift

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