JEE Main · Maths · Conic Sections

General Conic Section: JEE Main previous year questions

Name: General Conic Section: JEE Main previous year questions
Creator: Lumi

42 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 12 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 42; in 34 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 34 of 108 shifts: 42 questions, #77 of 196 topics.
02
45% of its questions since 2020 tested an idea no earlier year had asked; 15 repeated an idea from the year before.
03
The most repeated idea is Chord Bisected at a Given Point (T=S1), asked 7 times in 7 shifts (2021, 2024, 2026), most often as “chord with given midpoint on hyperbola”.
04
JEE Main has asked 16 of the 57 ideas in this topic; 32 have never been asked, directly or inside another question.
05
Mostly asked as single correct (64%); 36% need a numerical answer, 5% are easy and 33% hard.
06
The skill tested most is multi-step (83%), then application (14%).

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: 14 in 24 shifts · 2022: 14 in 24 shifts · 2023: 1 in 12 shifts · 2024: 6 in 18 shifts · 2025: 2 in 8 shifts · 2026: 4 in 9 shifts.

Up to 2023: 0.2; a shift, of 25
Since 2024: 0.3; 0.1
Usual gap: 1.0 yrs; between years asking it
Shifts with it: 34/108; 31% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 42 questions on General Conic Section since 2017.

Difficulty

QUESTIONS

2614

Easy2 · 5%
Medium26 · 62%
Hard14 · 33%

Format

Single correct · 27 Q64%
Numerical value · 15 Q36%

Skill tested

Multi-step · 35 Q83%
Application · 6 Q14%
Calculation · 1 Q2%

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 16 of the 57 ideas in this topic. 32 have never been asked yet.

16932

Asked directly16 · 28%
Touched inside another question9 · 16%
Never asked32 · 56%

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

OpenRepeated7 · 17%17%3/833
- 2 Apr ’26 S2 · Q11
  Let $O$ be the origin, and $P$ and $Q$ be two points on the rectangular hyperbola $xy = 12$ such that the midpoint of the line segment…
  mediumSingle correct
- 4 Apr ’26 S1 · Q13
  Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3y=0$ are bisected by the $y$ -axis. If the other ends of…
  hardSingle correct
- 6 Apr ’26 S2 · Q12
  Let $x=9$ be a directrix of an ellipse E, whose centre is at the origin and eccentricity is $\frac{1}{3}$ . Let P $(\alpha,0)$ , $\alpha>0$ ,…
  mediumSingle correct
- 4 Apr ’24 S2 · Q15
  Let PQ be a chord of the parabola $y^2=12x$ and the midpoint of PQ be at $(4,1)$ . Then, which of the following point lies on the line…
  mediumSingle correct
- 9 Apr ’24 S2 · Q27
  Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$ . If the set of all values of $\alpha$ , for which three chords of the…
  hardNumerical value
- 27 Jan ’24 S1 · Q16
  The length of the chord of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$ , whose mid point is $\left(1, \dfrac{2}{5}\right)$ , is equal to :
  hardSingle correct
- 26 Aug ’21 S2 · Q73
  Read the question
  hardSingle correctNew idea
OpenRepeated7 · 17%17%3/824
OpenRepeated6 · 14%14%3/823
OpenRepeated5 · 12%12%3/822
OpenRepeated4 · 10%10%3/82
OpenRepeated2 · 5%5%2/8
Open2 · 5%5%1/82
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%1/8
Open1 · 2%2%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

16 different ideas were tested; 7 came more than once.

Chord Bisected at a Given Point (T=S1)7×
chord with given midpoint on hyperbola
Single correct · 7 shifts · 1 numerical
Condition for Line to be Tangent7×
area of quadrilateral from ellipse tangents
Single correct · 6 shifts · 3 numerical
Tangent to General Conic (T=0)6×
locus then tangent intercepts
Single correct · 6 shifts · 2 numerical
Condition for a Circle5×
radius of circle that is mirror image in a line
Numerical value · 5 shifts · 4 numerical
Focus-Directrix Form Extraction4×
points on parabola from focus and directrix
Single correct · 4 shifts
Chord of Contact for General Conic2×
intersection of tangents at chord endpoints
Single correct · 2 shifts
Condition for Line Tangency2×
common tangent to parabola and ellipse
Single correct · 2 shifts
Vertex of Parabola from General Equation1×
max distance between points on circle and parabola vertex
Single correct · 1 shift
Condition for a Parabola1×
conic identified from tangent slope condition
Numerical value · 1 shift · 1 numerical
Family of Conics: Intersection of Two Conics1×
rectangle from intersection of two conics
Numerical value · 1 shift · 1 numerical
Pair of Tangents (SS1 = T^2)1×
tangents from external point to parabola
Numerical value · 1 shift · 1 numerical
Latus Rectum of a General Parabola1×
latus rectum of parabola from vertex and directrix
Single correct · 1 shift
Length of Intercept on a Line1×
intercept of circle on axis
Single correct · 1 shift
Condition for a Hyperbola1×
eccentricity of locus conic
Numerical value · 1 shift · 1 numerical
Equation of Director Circle1×
locus of perpendicular tangents
Single correct · 1 shift
Vertex of a General Parabola1×
line through centre of circle and vertex of parabola
Numerical value · 1 shift · 1 numerical

Idea	Times	Shifts	Format	Numerical
Chord Bisected at a Given Point (T=S1)chord with given midpoint on hyperbola	7	7	Single correctMulti-step	1
Condition for Line to be Tangentarea of quadrilateral from ellipse tangents	7	6	Single correctMulti-step	3
Tangent to General Conic (T=0)locus then tangent intercepts	6	6	Single correctMulti-step	2
Condition for a Circleradius of circle that is mirror image in a line	5	5	Numerical valueMulti-step	4
Focus-Directrix Form Extractionpoints on parabola from focus and directrix	4	4	Single correctMulti-step	–
Chord of Contact for General Conicintersection of tangents at chord endpoints	2	2	Single correctMulti-step	–
Condition for Line Tangencycommon tangent to parabola and ellipse	2	2	Single correctMulti-step	–
Vertex of Parabola from General Equationmax distance between points on circle and parabola vertex	1	1	Single correctMulti-step	–
Condition for a Parabolaconic identified from tangent slope condition	1	1	Numerical valueMulti-step	1
Family of Conics: Intersection of Two Conicsrectangle from intersection of two conics	1	1	Numerical valueMulti-step	1
Pair of Tangents (SS1 = T^2)tangents from external point to parabola	1	1	Numerical valueMulti-step	1
Latus Rectum of a General Parabolalatus rectum of parabola from vertex and directrix	1	1	Single correctCalculation	–
Length of Intercept on a Lineintercept of circle on axis	1	1	Single correctMulti-step	–
Condition for a Hyperbolaeccentricity of locus conic	1	1	Numerical valueMulti-step	1
Equation of Director Circlelocus of perpendicular tangents	1	1	Single correctApplication	–
Vertex of a General Parabolaline through centre of circle and vertex of parabola	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

General Conic Section 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

Idea, year, question

Every idea inside this topic

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JEE Main 20201 question in 1 shift

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