JEE Main · Maths · Three Dimensional Geometry

Skew Lines: JEE Main previous year questions

Name: Skew Lines: JEE Main previous year questions
Creator: Lumi

36 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 18 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 36; in 35 of 108 shifts
Years asked: 7/8; last asked 2026
Chance in a shift: 30%; calibrated model, how we compute it
Weighted estimate: 0.3; model; history: 0.3 a shift on average, typically 0.1–0.5

Key findings

01
Asked in 7 of 8 years with analysed shifts and in 35 of 108 shifts: 36 questions, #93 of 196 topics.
02
22% of its questions since 2020 tested an idea no earlier year had asked; 20 repeated an idea from the year before.
03
The most repeated idea is Cartesian Shortest Distance, asked 15 times in 15 shifts (2020, 2022, 2023, 2024, 2025, 2026), most often as “shortest distance between skew lines”.
04
JEE Main has asked 8 of the 63 ideas in this topic; 53 have never been asked, directly or inside another question.
05
Mostly asked as single correct (69%); 31% need a numerical answer, 17% are easy and 17% hard. It went up from 0.2 to 0.5 questions a shift since 2024.
06
The skill tested most is calculation (69%), then multi-step (28%).

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: 1 in 12 shifts · 2021: 4 in 24 shifts · 2022: 7 in 24 shifts · 2023: 6 in 12 shifts · 2024: 11 in 18 shifts · 2025: 5 in 8 shifts · 2026: 2 in 9 shifts.

Up to 2023: 0.2; a shift, of 25
Since 2024: 0.5; 0.3
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 35/108; 32% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 36 questions on Skew Lines since 2017.

Difficulty

QUESTIONS

6246

Easy6 · 17%
Medium24 · 67%
Hard6 · 17%

Format

Single correct · 25 Q69%
Numerical value · 11 Q31%

Skill tested

Calculation · 25 Q69%
Multi-step · 10 Q28%
Application · 1 Q3%

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 8 of the 63 ideas in this topic. 53 have never been asked yet.

853

Asked directly8 · 13%
Touched inside another question2 · 3%
Never asked53 · 84%

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

OpenRepeated15 · 42%42%6/8426
- 6 Apr ’26 S2 · Q14
  The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is :
  easySingle correctAsked the year before
- 7 Apr ’25 S1 · Q14
  If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and…
  mediumSingle correctAsked the year before
- 8 Apr ’24 S2 · Q16
  If the shortest distance between the lines $\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4}$ and…
  mediumSingle correctAsked the year before
- 9 Apr ’24 S1 · Q16
  The shortest distance between the lines $\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}$ and $\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}$ is :
  easySingle correctAsked the year before
- 1 Feb ’24 S1 · Q16
  If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and…
  mediumSingle correctAsked the year before
- 27 Jan ’24 S1 · Q18
  If the shortest distance between the lines $\dfrac{x-4}{1}=\dfrac{y+1}{2}=\dfrac{z}{-3}$ and…
  mediumSingle correctAsked the year before
- 30 Jan ’24 S1 · Q28
  If $d_1$ is the shortest distance between the lines $x+1=2y=-12z$ , $x=y+2=6z-6$ and $d_2$ is the shortest distance between the lines…
  mediumNumerical valueAsked the year before
- 31 Jan ’24 S2 · Q17
  The shortest distance, between lines $L_1$ and $L_2$ , where $L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2}$ and $L_2$ is the line,…
  mediumSingle correctAsked the year before
- 10 Apr ’23 S1 · Q15
  The shortest distance between the lines $\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}$ and $\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}$ is
  easySingle correctAsked the year before
- 15 Apr ’23 S1 · Q15
  Let S be the set of all values of $\lambda$ , for which the shortest distance between the lines…
  mediumSingle correctAsked the year before
- 25 Jul ’22 S2 · Q16
  The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is
  mediumSingle correct
- 30 Jul ’22 S2 · Q87
  Let $L_1$ be a line in the $yz$ - plane with $y$ and $z$ intercepts $\frac{1}{4}$ and $\frac{1}{C}$ $(C > 0)$ respectively. Let $L_2$ be…
  hardNumerical value
- 24 Jun ’22 S2 · Q14
  If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{\lambda}$ and…
  mediumSingle correct
- 27 Jun ’22 S2 · Q14
  Read the question
  mediumSingle correct
- 8 Jan ’20 S1 · Q65
  Read the question
  mediumSingle correctNew idea
OpenRepeated9 · 25%25%5/8232
OpenRepeated5 · 14%14%3/83
OpenRepeated3 · 8%8%3/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%1/8
Open1 · 3%3%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

8 different ideas were tested; 4 came more than once.

Cartesian Shortest Distance15×
shortest distance between skew lines
Single correct · 15 shifts · 2 numerical
Vector Shortest Distance Formula9×
shortest distance between skew lines
Single correct · 9 shifts · 4 numerical
Coplanarity Determinant Test5×
identify line coplanar with given line
Single correct · 5 shifts · 2 numerical
Finding an Unknown Parameter from Shortest Distance3×
unknown parameter from skew distance then circle radius
Single correct · 3 shifts · 1 numerical
Solve for Parameter Given Shortest Distance1×
parameter from shortest distance of lines
Single correct · 1 shift
Equation of Shortest Distance Line1×
foot points of shortest distance line
Numerical value · 1 shift · 1 numerical
Shortest Distance Between Cube Diagonals1×
shortest distance between diagonal and edge of cuboid
Single correct · 1 shift
Plane Containing One Line and Parallel to Other1×
plane containing one line parallel to another
Numerical value · 1 shift · 1 numerical

Idea	Times	Shifts	Format	Numerical
Cartesian Shortest Distanceshortest distance between skew lines	15	15	Single correctCalculation	2
Vector Shortest Distance Formulashortest distance between skew lines	9	9	Single correctCalculation	4
Coplanarity Determinant Testidentify line coplanar with given line	5	5	Single correctMulti-step	2
Finding an Unknown Parameter from Shortest Distanceunknown parameter from skew distance then circle radius	3	3	Single correctCalculation	1
Solve for Parameter Given Shortest Distanceparameter from shortest distance of lines	1	1	Single correctMulti-step	–
Equation of Shortest Distance Linefoot points of shortest distance line	1	1	Numerical valueCalculation	1
Shortest Distance Between Cube Diagonalsshortest distance between diagonal and edge of cuboid	1	1	Single correctCalculation	–
Plane Containing One Line and Parallel to Otherplane containing one line parallel to another	1	1	Numerical valueMulti-step	1

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

Skew Lines 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

Skew Lines questions, year by year

JEE Main 20262 questions in 2 shifts

JEE Main 20255 questions in 5 shifts

JEE Main 202411 questions in 10 shifts

JEE Main 20236 questions in 6 shifts

JEE Main 20227 questions in 7 shifts

JEE Main 20214 questions in 4 shifts

JEE Main 20201 question in 1 shift

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