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Sunday, 25 October

JEE Main · Maths · Class 11

Conic Sections: JEE Main previous year questions

296 questions in 107 of the 108 JEE Main shifts Lumi analysed, asked in 8 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
296
in 107 of 108 shifts · 8 of 8 years
Average a shift
2.4
of 25 Maths · 2.8 since 2024 +0.6
Typical range
2.0–3.1
questions a shift; fewest 1.7, most 3.3
Weighted estimate
2.7
model, recent years count more · about 10.7 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Conic Sections

Priority

Must do

One of the 8 Maths chapters that together held the first half of Maths questions in the 108 shifts analysed. How bands are set

Past questions
296in 107 of 108 shifts
Study plan gives it
41 hover 12 months; 31 h over 6
Study this chapter →

Ideas asked most often

  1. Length of Latus Rectum12×
  2. Eccentricity calculation11×
  3. Condition of tangency11×
  4. Common Tangent to Circle and Conic9×
  5. Family of Circles Touching a Line8×

306 of the 415 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 37% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Conic Sections at a glance

  1. 01

    63%

    of its 62 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    74%

    of the 415 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    30%

    of its questions asked for a numerical answer, 1.0 times the Maths average.

  4. 04

    35%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

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.

0241.7’172.3’202.3’212.6’222’232.1’243.3’253.1’26

Raw count: 2017: 2 in 1 shift · 2020: 28 in 12 shifts · 2021: 65 in 24 shifts · 2022: 74 in 24 shifts · 2023: 28 in 12 shifts · 2024: 45 in 18 shifts · 2025: 26 in 8 shifts · 2026: 28 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step56%
  • Numerical answer30%
  • Application7%
  • Calculation6%
  • Conceptual1%

Most common asks: relation between conic eccentricities (3); chord length of circle cut by line (2); locus of midpoint on parabola (2).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#1
of 70 by weighted estimate
Rank in Maths
#1
of 21 chapters
Share of Maths
9.7%
of its questions, all shifts analysed
Busiest year
2025
3.3 questions a shift
Year to year
Steady
varies by about 0.5 questions a shift
Long-run direction
+0.13
questions a shift, per year
Easy questions
7%
35% rated hard
Numerical answer
30%
1.0× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
41 h
31 h on a 6-month plan
Marks per study hour
0.26
#10 of 70 chapters
Foundation for others
48%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20172
  • 202028
  • 202165
  • 202274
  • 202328
  • 202445
  • 202526
  • 202628
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step83%
  • Calculation9%
  • Application7%
  • Conceptual1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 415 ideas. In the 108 shifts analysed, JEE Main built a question around 77 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
77
Touched on in a question
32
Never asked
306

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 88 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
018+questions in that year’s analysed shifts, shaded per shift
  • Circle Tangents

    As a topic: 62 questions in 7 of 8 years, most often single correct, 40% numerical answer.

  • Ellipse Eccentricity

    As a topic: 47 questions in 7 of 8 years, most often single correct, 17% numerical answer.

  • General Conic Section

    As a topic: 42 questions in 7 of 8 years, most often single correct, 36% numerical answer.

  • Normals to Conics

    As a topic: 16 questions in 7 of 8 years, most often single correct, 25% numerical answer.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open59 · 20%71816782

    19 ideas inside

    • OpenRepeated9 · 15%342
    • OpenRepeated9 · 15%52
    • OpenRepeated8 · 14%23
    • OpenRepeated6 · 10%3
    • OpenRepeated5 · 8%23
    • OpenRepeated5 · 8%2
    • OpenRepeated3 · 5%2
    • OpenRepeated3 · 5%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
    • Open1 · 2%
  • Open46 · 16%77931073
  • Open42 · 14%1414624
  • Open15 · 5%434
  • Open12 · 4%4222
  • Open10 · 3%44
  • Open9 · 3%232
  • Open6 · 2%2
  • Open3 · 1%
  • Open2 · 1%
  • Open2 · 1%2
  • Open1 · 0%
  • Open1 · 0%

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

The exact ideas JEE Main has asked

Inside the topics, 84 different ideas were tested; 33 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 296 Conic Sections questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 202628 questions

  1. 2 Apr 2026, Shift 1 · Q10Let an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a<ba<b, pass through the point (4,3)(4, 3) and have eccentricity 53\frac{\sqrt5}{3}. Then…MediumSingle correct
  2. 2 Apr 2026, Shift 1 · Q24Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts…HardNumerical value
  3. 2 Apr 2026, Shift 2 · Q10Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines…MediumSingle correct
  4. 2 Apr 2026, Shift 2 · Q11Let OO be the origin, and PP and QQ be two points on the rectangular hyperbola xy=12xy = 12 such that the midpoint of the line segment…MediumSingle correct
  5. 2 Apr 2026, Shift 2 · Q12Let the parabola y=x2+px+qy = x^2 + px + q passing through the point (1,−1)(1, -1) be such that the distance between its vertex and the xx-axis is…MediumSingle correct
  6. 2 Apr 2026, Shift 2 · Q23Let AA be the point (3,0)(3, 0) and circles with variable diameter ABAB touch the circle x2+y2=36x^2 + y^2 = 36 internally. Let the curve CC be…HardNumerical value
  7. 4 Apr 2026, Shift 1 · Q13Suppose that two chords, drawn from the point (1,2)(1,2) on the circle x2+y2+x−3y=0x^2+y^2+x-3y=0 are bisected by the yy-axis. If the other ends of…HardSingle correct
  8. 4 Apr 2026, Shift 1 · Q22Consider the parabola P:y2=4kxP: y^2=4kx and the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1. Let the line segment joining the points of…MediumNumerical value
  9. 4 Apr 2026, Shift 2 · Q10Let P(3cos⁡α,2sin⁡α)P(3\cos\alpha,2\sin\alpha), α≠0\alpha\neq0, be a point on the ellipse x29+y24=1\frac{x^2}{9}+\frac{y^2}{4}=1, QQ be a point on the circle…HardSingle correct
  10. 4 Apr 2026, Shift 2 · Q11Let H:x2a2−y2b2=1H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 be a hyperbola such that the distance between its foci is 6 and the distance between its…MediumSingle correct
  11. 4 Apr 2026, Shift 2 · Q24Let A,BA,B and CC be the vertices of a variable right angled triangle inscribed in the parabola y2=16xy^2=16x. Let the vertex BB containing…HardNumerical value
  12. 5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 be S(4,0)S(4, 0) and its eccentricity be 45\frac{4}{5}. If the point…EasySingle correct
  13. 5 Apr 2026, Shift 1 · Q10Let P be a moving point on the circle x2+y2−6x−8y+21=0x^2 + y^2 - 6x - 8y + 21 = 0. Then, the maximum distance of P from the vertex of the parabola…MediumSingle correct
  14. 5 Apr 2026, Shift 2 · Q11Let the point P be the vertex of the parabola y=x2−6x+12y=x^2-6x+12. If a line passing through the point P intersects the circle…HardSingle correct
  15. 5 Apr 2026, Shift 2 · Q12Let the directrix of the parabola P:y2=8xP: y^2=8x, cut x-axis at the point A. Let B(α,β)B(\alpha, \beta), α>1\alpha>1, be a point on P such that…MediumSingle correct
  16. 5 Apr 2026, Shift 2 · Q13Let the eccentricity e of a hyperbola satisfy the equation 6e2−11e+3=06e^2-11e+3=0. If the foci of the hyperbola are (3,5)(3, 5) and (3,−4)(3, -4), then…MediumSingle correct
  17. 6 Apr 2026, Shift 1 · Q2Let one root of the quadratic equation in xx: (k2−15k+27)x2+9(k−1)x+18=0(k^2-15k+27)x^2+9(k-1)x+18=0 be twice the other. Then the length of the latus rectum of…MediumSingle correct
  18. 6 Apr 2026, Shift 1 · Q3Let e1e_1 and e2e_2 be two distinct roots of the equation x2−ax+2=0x^2-ax+2=0. Let the sets {a∈R:e1\{a\in\mathbb{R}: e_1 and e2e_2 are the…HardSingle correct
  19. 6 Apr 2026, Shift 1 · Q11If the eccentricity ee of the hyperbola x2a2−y2b2=1\frac{x^2}{a^2}-\frac{y^2}{b^2}=1, passing through (6,43)\left(6,4\sqrt{3}\right), satisfies…MediumSingle correct
  20. 6 Apr 2026, Shift 1 · Q12Let chord PQ of length 3133\sqrt{13} of the parabola y2=12xy^2=12x be such that the ordinates of points P and Q are in the ratio 1:2. If the…HardSingle correct
  21. 6 Apr 2026, Shift 1 · Q22Let the centre of the circle x2+y2+2gx+2fy+25=0x^2+y^2+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x−y=42x-y=4. Let the area of an equilateral…MediumNumerical value
  22. 6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the xx-axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
  23. 6 Apr 2026, Shift 2 · Q11The eccentricity of an ellipse E with centre at the origin O is 32\frac{\sqrt{3}}{2} and its directrices are x=±463x=\pm\frac{4\sqrt{6}}{3}.…MediumSingle correct
  24. 6 Apr 2026, Shift 2 · Q12Let x=9x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 13\frac{1}{3}. Let P (α,0)(\alpha,0), α>0\alpha>0,…MediumSingle correct
  25. 6 Apr 2026, Shift 2 · Q23Let the line x−y=4x-y=4 intersect the circle C : (x−4)2+(y+3)2=9(x-4)^2+(y+3)^2=9 at the points Q and R. If P(α,β)(\alpha,\beta) is a point on C such that PQ…MediumNumerical value
  26. 8 Apr 2026, Shift 2 · Q11Let O be the vertex of the parabola y2=4xy^2 = 4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of…MediumSingle correct
  27. 8 Apr 2026, Shift 2 · Q20Let x2f(a2+7a+3)+y2f(3a+15)=1\frac{x^2}{f(a^2 + 7a + 3)} + \frac{y^2}{f(3a + 15)} = 1 represent an ellipse with major axis along yy-axis, where ff is a…HardSingle correct
  28. 8 Apr 2026, Shift 2 · Q24Consider the circle C:x2+y2−6x−8y−11=0C : x^2 + y^2 - 6x - 8y - 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin. If…HardNumerical value

JEE Main 202526 questions

  1. 2 Apr 2025, Shift 1 · Q1Let the focal chord PQ of the parabola y2=4xy^2=4x make an angle of 60∘60^\circ with the positive xx-axis, where P lies in the first…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q4If S and S' are the foci of the ellipse x218+y29=1\frac{x^2}{18}+\frac{y^2}{9}=1 and P be a point on the ellipse, then…MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q10Let one focus of the hyperbola H:x2a2−y2b2=1\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 be at (10,0)(\sqrt{10},0) and the corresponding directrix be…EasySingle correct
  4. 2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point (−9,4)(-9, 4) and touching the lines…HardNumerical value
  5. 2 Apr 2025, Shift 2 · Q11Let the point PP of the focal chord PQPQ of the parabola y2=16xy^2 = 16x be (1,−4)(1, -4). If the focus of the parabola divides the chord PQPQ in…MediumSingle correct
  6. 2 Apr 2025, Shift 2 · Q12If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the…EasySingle correct
  7. 3 Apr 2025, Shift 1 · Q11The radius of the smallest circle which touches the parabolas y=x2+2y = x^2 + 2 and x=y2+2x = y^2 + 2 isHardSingle correct
  8. 3 Apr 2025, Shift 1 · Q12A line passing through the point P(5,5)P(\sqrt{5}, \sqrt{5}) intersects the ellipse x236+y225=1\frac{x^2}{36} + \frac{y^2}{25} = 1 at AA and BB such…HardSingle correct
  9. 3 Apr 2025, Shift 1 · Q23Let the product of the focal distances of the point P(4,23)\mathrm{P}\left(4, 2\sqrt{3}\right) on the hyperbola…MediumNumerical value
  10. 3 Apr 2025, Shift 2 · Q11If the four distinct points (4,6),(−1,5),(0,0)(4, 6), (-1, 5), (0, 0) and (k,3k)(k, 3k) lie on a circle of radius rr, then 10k+r210k + r^2 is equal toMediumSingle correct
  11. 3 Apr 2025, Shift 2 · Q12Let CC be the circle of minimum area enclosing the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 with eccentricity 12\frac{1}{2} and…HardSingle correct
  12. 3 Apr 2025, Shift 2 · Q23If the equation of the hyperbola with foci (4,2)(4, 2) and (8,2)(8, 2) is 3x2−y2−αx+βy+γ=03x^2 - y^2 - \alpha x + \beta y + \gamma = 0, then…MediumNumerical value
  13. 4 Apr 2025, Shift 2 · Q9Open the question · Hard · Single correct
  14. 4 Apr 2025, Shift 2 · Q10Condition for Line to be Tangent · Hard · Single correct
  15. 4 Apr 2025, Shift 2 · Q11Focal distance property · Hard · Single correct
  16. 4 Apr 2025, Shift 2 · Q12Open the question · Hard · Single correct
  17. 4 Apr 2025, Shift 2 · Q19Area Involving Tangents and Normals · Medium · Single correct
  18. 7 Apr 2025, Shift 1 · Q10Focus-Directrix Form Extraction · Medium · Single correct
  19. 7 Apr 2025, Shift 1 · Q12Common Tangent of Touching Circles · Medium · Single correct
  20. 7 Apr 2025, Shift 1 · Q23Open the question · Hard · Numerical value
  21. 7 Apr 2025, Shift 2 · Q1Open the question · Medium · Single correct
  22. 7 Apr 2025, Shift 2 · Q12Length of Latus Rectum · Medium · Single correct
  23. 7 Apr 2025, Shift 2 · Q13Coordinates of foci · Medium · Single correct
  24. 7 Apr 2025, Shift 2 · Q22Open the question · Hard · Numerical value
  25. 8 Apr 2025, Shift 2 · Q12Product of Focal Distances · Medium · Single correct
  26. 8 Apr 2025, Shift 2 · Q23Open the question · Hard · Numerical value

JEE Main 202445 questions

  1. 4 Apr 2024, Shift 1 · Q15Open the question · Hard · Single correct
  2. 4 Apr 2024, Shift 1 · Q28Focal Chord Length via Vertex Distance · Medium · Numerical value
  3. 4 Apr 2024, Shift 2 · Q13Open the question · Medium · Single correct
  4. 4 Apr 2024, Shift 2 · Q14Open the question · Hard · Single correct
  5. 4 Apr 2024, Shift 2 · Q15Chord Bisected at a Given Point (T=S1) · Medium · Single correct
  6. 5 Apr 2024, Shift 1 · Q13Maximum and Minimum Distance to a Circle · Medium · Single correct
  7. 5 Apr 2024, Shift 1 · Q15Length of Latus Rectum · Medium · Single correct
  8. 5 Apr 2024, Shift 1 · Q28Focal Chord Length via Slope · Medium · Numerical value
  9. 5 Apr 2024, Shift 2 · Q15Radical axis of two circles · Easy · Single correct
  10. 5 Apr 2024, Shift 2 · Q24Maximum and Minimum Distance to a Circle · Hard · Numerical value
  11. 5 Apr 2024, Shift 2 · Q27Point of Tangency from Given Slope · Medium · Numerical value
  12. 6 Apr 2024, Shift 1 · Q15Open the question · Easy · Single correct
  13. 6 Apr 2024, Shift 1 · Q26Pair of Tangents (SS1 = T^2) · Hard · Numerical value
  14. 6 Apr 2024, Shift 1 · Q27Condition for a Parabola · Hard · Numerical value
  15. 8 Apr 2024, Shift 1 · Q15Common Tangent of Touching Circles · Medium · Single correct
  16. 8 Apr 2024, Shift 1 · Q16Open the question · Medium · Single correct
  17. 8 Apr 2024, Shift 2 · Q28Open the question · Medium · Numerical value
  18. 9 Apr 2024, Shift 1 · Q12Length of Latus Rectum · Easy · Single correct
  19. 9 Apr 2024, Shift 1 · Q13Open the question · Medium · Single correct
  20. 9 Apr 2024, Shift 1 · Q29Common Tangent of Touching Circles · Hard · Numerical value
  21. 9 Apr 2024, Shift 2 · Q15Coordinates of foci · Medium · Single correct
  22. 9 Apr 2024, Shift 2 · Q27Chord Bisected at a Given Point (T=S1) · Hard · Numerical value
  23. 9 Apr 2024, Shift 2 · Q28Open the question · Hard · Numerical value
  24. 1 Feb 2024, Shift 1 · Q12Eccentricity calculation · Medium · Single correct
  25. 1 Feb 2024, Shift 1 · Q13Length of Latus Rectum · Medium · Single correct
  26. 1 Feb 2024, Shift 1 · Q15Number of Common Tangents · Medium · Single correct
  27. 1 Feb 2024, Shift 1 · Q29Condition of tangency · Hard · Numerical value
  28. 1 Feb 2024, Shift 2 · Q13Eccentricity calculation · Hard · Single correct
  29. 1 Feb 2024, Shift 2 · Q14Locus of Midpoint of Chords of Contact · Medium · Single correct
  30. 27 Jan 2024, Shift 1 · Q10Shortest Distance from Point to Parabola · Medium · Single correct
  31. 27 Jan 2024, Shift 1 · Q14Open the question · Medium · Single correct
  32. 27 Jan 2024, Shift 1 · Q16Chord Bisected at a Given Point (T=S1) · Hard · Single correct
  33. 29 Jan 2024, Shift 1 · Q27Condition of tangency · Medium · Numerical value
  34. 29 Jan 2024, Shift 1 · Q28Family of Conics: Intersection of Two Conics · Hard · Numerical value
  35. 30 Jan 2024, Shift 1 · Q14Open the question · Medium · Single correct
  36. 30 Jan 2024, Shift 1 · Q15Eccentricity when Foci Distance Equals Minor Axis · Medium · Single correct
  37. 30 Jan 2024, Shift 1 · Q27Open the question · Medium · Numerical value
  38. 30 Jan 2024, Shift 2 · Q14Equations of directrices · Medium · Single correct
  39. 30 Jan 2024, Shift 2 · Q15Open the question · Medium · Single correct
  40. 30 Jan 2024, Shift 2 · Q28Length of Common Chord via Radical Axis · Hard · Numerical value
  41. 31 Jan 2024, Shift 1 · Q13Open the question · Medium · Single correct
  42. 31 Jan 2024, Shift 1 · Q16Open the question · Hard · Single correct
  43. 31 Jan 2024, Shift 1 · Q28Length of Latus Rectum · Medium · Numerical value
  44. 31 Jan 2024, Shift 2 · Q10Optimization via AM-GM Inequality · Medium · Single correct
  45. 31 Jan 2024, Shift 2 · Q14Length of Latus Rectum · Hard · Single correct

JEE Main 202328 questions

  1. 6 Apr 2023, Shift 1 · Q27Open the question · Hard · Numerical value
  2. 6 Apr 2023, Shift 1 · Q28Equation of Tangent · Medium · Numerical value
  3. 6 Apr 2023, Shift 2 · Q2Eccentricity calculation · Easy · Single correct
  4. 6 Apr 2023, Shift 2 · Q13Area of Tangent-Chord Triangle · Medium · Single correct
  5. 6 Apr 2023, Shift 2 · Q27Length of Latus Rectum · Hard · Numerical value
  6. 8 Apr 2023, Shift 1 · Q14Equation of focal chord · Hard · Single correct
  7. 8 Apr 2023, Shift 1 · Q27Condition for a Circle · Medium · Numerical value
  8. 8 Apr 2023, Shift 2 · Q11Circumcircle of Tangent Triangle · Medium · Single correct
  9. 8 Apr 2023, Shift 2 · Q12Incenter via Equidistance · Hard · Single correct
  10. 8 Apr 2023, Shift 2 · Q29Open the question · Hard · Numerical value
  11. 10 Apr 2023, Shift 1 · Q11Open the question · Medium · Single correct
  12. 10 Apr 2023, Shift 1 · Q12Open the question · Hard · Single correct
  13. 10 Apr 2023, Shift 1 · Q29Common Tangent to Circle and Conic · Medium · Numerical value
  14. 10 Apr 2023, Shift 2 · Q12Open the question · Medium · Single correct
  15. 10 Apr 2023, Shift 2 · Q13Common Tangent to Circle and Conic · Hard · Single correct
  16. 11 Apr 2023, Shift 1 · Q3Open the question · Hard · Single correct
  17. 11 Apr 2023, Shift 1 · Q28Open the question · Medium · Numerical value
  18. 11 Apr 2023, Shift 2 · Q14Open the question · Hard · Single correct
  19. 11 Apr 2023, Shift 2 · Q27Hyperbola Normal Point Form · Hard · Numerical value
  20. 12 Apr 2023, Shift 1 · Q12Open the question · Hard · Single correct
  21. 12 Apr 2023, Shift 1 · Q28Open the question · Hard · Numerical value
  22. 13 Apr 2023, Shift 1 · Q15Equation of Polar · Hard · Single correct
  23. 13 Apr 2023, Shift 1 · Q16Focal Chord Length via Slope · Hard · Single correct
  24. 13 Apr 2023, Shift 1 · Q26Open the question · Hard · Numerical value
  25. 13 Apr 2023, Shift 2 · Q13Normal Passes Through Center · Medium · Single correct
  26. 13 Apr 2023, Shift 2 · Q28Open the question · Hard · Numerical value
  27. 15 Apr 2023, Shift 1 · Q13Number of Common Tangents · Easy · Single correct
  28. 15 Apr 2023, Shift 1 · Q28Eccentricity from Minor Axis Subtended Angle · Medium · Numerical value

JEE Main 202274 questions

  1. 25 Jul 2022, Shift 1 · Q13Area of Locus-Defined Regions · Medium · Single correct
  2. 25 Jul 2022, Shift 1 · Q28Condition for Line to be Tangent · Medium · Numerical value
  3. 25 Jul 2022, Shift 1 · Q29Family of Circles Touching a Line · Hard · Numerical value
  4. 25 Jul 2022, Shift 2 · Q12Eccentricity calculation · Easy · Single correct
  5. 25 Jul 2022, Shift 2 · Q13Tangent to General Conic (T=0) · Medium · Single correct
  6. 25 Jul 2022, Shift 2 · Q14Coordinates of foci · Medium · Single correct
  7. 25 Jul 2022, Shift 2 · Q28Common Tangent of Touching Circles · Medium · Numerical value
  8. 26 Jul 2022, Shift 1 · Q12Condition for a Circle · Medium · Single correct
  9. 26 Jul 2022, Shift 1 · Q13Hyperbola Normal Point Form · Medium · Single correct
  10. 26 Jul 2022, Shift 2 · Q11Combined Equation of Tangents (SS1=T^2) · Hard · Single correct
  11. 26 Jul 2022, Shift 2 · Q12Common Tangents to Two Curves · Medium · Single correct
  12. 26 Jul 2022, Shift 2 · Q13Open the question · Medium · Single correct
  13. 26 Jul 2022, Shift 2 · Q14Open the question · Medium · Single correct
  14. 27 Jul 2022, Shift 1 · Q11Tangent to General Conic (T=0) · Medium · Single correct
  15. 27 Jul 2022, Shift 1 · Q19Length of Intercept on a Line · Medium · Single correct
  16. 27 Jul 2022, Shift 1 · Q24Length of Latus Rectum · Hard · Numerical value
  17. 27 Jul 2022, Shift 1 · Q29Length of Latus Rectum · Medium · Numerical value
  18. 27 Jul 2022, Shift 2 · Q12Tangent at a point (T=0) · Medium · Single correct
  19. 27 Jul 2022, Shift 2 · Q13Open the question · Medium · Single correct
  20. 27 Jul 2022, Shift 2 · Q29Common Tangents to Two Curves · Hard · Numerical value
  21. 28 Jul 2022, Shift 1 · Q11Chord of Contact for General Conic · Hard · Single correct
  22. 28 Jul 2022, Shift 1 · Q12Open the question · Medium · Single correct
  23. 28 Jul 2022, Shift 1 · Q27Condition for Line to be Tangent · Hard · Numerical value
  24. 28 Jul 2022, Shift 2 · Q73Area of Tangent-Chord Triangle · Medium · Single correct
  25. 28 Jul 2022, Shift 2 · Q74Open the question · Hard · Single correct
  26. 28 Jul 2022, Shift 2 · Q83Focal distance property · Hard · Numerical value
  27. 28 Jul 2022, Shift 2 · Q85Common Tangent to Circle and Conic · Hard · Numerical value
  28. 29 Jul 2022, Shift 1 · Q17Equation of focal chord · Hard · Single correct
  29. 29 Jul 2022, Shift 1 · Q30Reflection of Center Across Tangent · Medium · Numerical value
  30. 29 Jul 2022, Shift 2 · Q28Chord of contact · Medium · Numerical value
  31. 29 Jul 2022, Shift 2 · Q30Open the question · Hard · Numerical value
  32. 30 Jul 2022, Shift 2 · Q75Open the question · Medium · Single correct
  33. 30 Jul 2022, Shift 2 · Q76Open the question · Hard · Single correct
  34. 30 Jul 2022, Shift 2 · Q86Tangent to General Conic (T=0) · Medium · Numerical value
  35. 24 Jun 2022, Shift 1 · Q5Common Tangent to Circle and Conic · Hard · Single correct
  36. 24 Jun 2022, Shift 1 · Q15Condition for Line to be Tangent · Medium · Single correct
  37. 24 Jun 2022, Shift 1 · Q28Condition for Line to be Tangent · Hard · Numerical value
  38. 24 Jun 2022, Shift 2 · Q9Maximum Inscribed Rectangle Area via Eccentricity · Hard · Single correct
  39. 24 Jun 2022, Shift 2 · Q27Family of Circles Touching a Line · Medium · Numerical value
  40. 24 Jun 2022, Shift 2 · Q29Length of Latus Rectum · Medium · Numerical value
  41. 24 Jun 2022, Shift 2 · Q30Reflection of a Line in a Line · Medium · Numerical value
  42. 25 Jun 2022, Shift 1 · Q1Family of Circles Touching a Line · Medium · Single correct
  43. 25 Jun 2022, Shift 1 · Q16Common Tangent to Circle and Conic · Hard · Single correct
  44. 25 Jun 2022, Shift 1 · Q19Focus-Directrix Form Extraction · Hard · Single correct
  45. 25 Jun 2022, Shift 1 · Q24Condition for a Circle · Medium · Numerical value
  46. 25 Jun 2022, Shift 2 · Q10Open the question · Medium · Single correct
  47. 25 Jun 2022, Shift 2 · Q18Condition for a Line to Touch a Curve · Medium · Single correct
  48. 25 Jun 2022, Shift 2 · Q20Open the question · Medium · Single correct
  49. 25 Jun 2022, Shift 2 · Q29Hyperbola Normal Point Form · Hard · Numerical value
  50. 26 Jun 2022, Shift 1 · Q12Open the question · Medium · Single correct
  51. 26 Jun 2022, Shift 1 · Q13Parabola Normal Parametric Form · Medium · Single correct
  52. 26 Jun 2022, Shift 1 · Q23Common Tangent to Circle and Conic · Hard · Numerical value
  53. 26 Jun 2022, Shift 2 · Q11Common Tangents to Two Curves · Medium · Single correct
  54. 26 Jun 2022, Shift 2 · Q12Open the question · Medium · Single correct
  55. 26 Jun 2022, Shift 2 · Q13Hyperbola Normal Point Form · Medium · Single correct
  56. 26 Jun 2022, Shift 2 · Q29Open the question · Hard · Numerical value
  57. 27 Jun 2022, Shift 1 · Q13Eccentricity calculation · Easy · Single correct
  58. 27 Jun 2022, Shift 1 · Q28Open the question · Medium · Numerical value
  59. 27 Jun 2022, Shift 1 · Q29Open the question · Hard · Numerical value
  60. 27 Jun 2022, Shift 2 · Q11Focus-Directrix Form Extraction · Medium · Single correct
  61. 27 Jun 2022, Shift 2 · Q12Open the question · Medium · Single correct
  62. 28 Jun 2022, Shift 1 · Q13Open the question · Medium · Single correct
  63. 28 Jun 2022, Shift 1 · Q14Area of Tangent-Chord Triangle · Medium · Single correct
  64. 28 Jun 2022, Shift 1 · Q30Normal Passes Through Center · Hard · Numerical value
  65. 28 Jun 2022, Shift 2 · Q13Open the question · Medium · Single correct
  66. 28 Jun 2022, Shift 2 · Q15Latus Rectum of a General Parabola · Easy · Single correct
  67. 28 Jun 2022, Shift 2 · Q23Length of Common Chord via Radical Axis · Medium · Numerical value
  68. 29 Jun 2022, Shift 1 · Q18Equation of focal chord · Hard · Single correct
  69. 29 Jun 2022, Shift 1 · Q19Area of Tangent-Chord Triangle · Hard · Single correct
  70. 29 Jun 2022, Shift 1 · Q28Open the question · Medium · Numerical value
  71. 29 Jun 2022, Shift 2 · Q10Chord of Contact from Directrix is Focal · Hard · Single correct
  72. 30 Jun 2022, Shift 1 · Q14Condition of tangency · Hard · Single correct
  73. 30 Jun 2022, Shift 1 · Q15Eccentricity calculation · Hard · Single correct
  74. 30 Jun 2022, Shift 1 · Q27Length of focal chord · Medium · Numerical value

JEE Main 202165 questions

  1. 3 Aug 2021, Shift 1 · Q73Condition for Line to be Tangent · Medium · Single correct
  2. 3 Aug 2021, Shift 1 · Q74Intersection of Tangents at Focal Chord Extremities · Hard · Single correct
  3. 3 Aug 2021, Shift 2 · Q74Focal distance property · Medium · Single correct
  4. 3 Aug 2021, Shift 2 · Q75Chord of Contact for General Conic · Medium · Single correct
  5. 3 Aug 2021, Shift 2 · Q86Coordinates of Point of Contact · Medium · Numerical value
  6. 4 Aug 2021, Shift 1 · Q73Family of Circles Touching a Line · Medium · Single correct
  7. 4 Aug 2021, Shift 1 · Q74Open the question · Easy · Single correct
  8. 4 Aug 2021, Shift 1 · Q75Angle Between Curves · Hard · Single correct
  9. 4 Aug 2021, Shift 2 · Q72Equation of Chord with Given Midpoint (T = S1) · Hard · Single correct
  10. 4 Aug 2021, Shift 2 · Q73Intercepts of Tangent and Normal · Medium · Single correct
  11. 4 Aug 2021, Shift 2 · Q74Hyperbola Normal Parametric Form · Hard · Single correct
  12. 26 Aug 2021, Shift 1 · Q73Tangent in slope form · Hard · Single correct
  13. 26 Aug 2021, Shift 1 · Q74Area of Foci-Minor Axis Triangle · Hard · Single correct
  14. 26 Aug 2021, Shift 1 · Q90Open the question · Medium · Numerical value
  15. 26 Aug 2021, Shift 2 · Q71Family of Circles Touching a Line · Hard · Single correct
  16. 26 Aug 2021, Shift 2 · Q72Tangent to General Conic (T=0) · Hard · Single correct
  17. 26 Aug 2021, Shift 2 · Q73Chord Bisected at a Given Point (T=S1) · Hard · Single correct
  18. 27 Aug 2021, Shift 1 · Q70Parabola Normal Point Form · Medium · Single correct
  19. 27 Aug 2021, Shift 1 · Q86Condition for a Circle · Hard · Numerical value
  20. 27 Aug 2021, Shift 1 · Q87Optimizing Tangent-Bounded Area · Medium · Numerical value
  21. 27 Aug 2021, Shift 2 · Q75Equation of Director Circle · Medium · Single correct
  22. 27 Aug 2021, Shift 2 · Q85Common Tangent of Touching Circles · Medium · Numerical value
  23. 27 Aug 2021, Shift 2 · Q86Hyperbola Normal Parametric Form · Hard · Numerical value
  24. 31 Aug 2021, Shift 1 · Q74Open the question · Easy · Single correct
  25. 31 Aug 2021, Shift 1 · Q75Open the question · Medium · Single correct
  26. 31 Aug 2021, Shift 1 · Q86Condition of tangency · Hard · Numerical value
  27. 31 Aug 2021, Shift 2 · Q73Open the question · Medium · Single correct
  28. 31 Aug 2021, Shift 2 · Q88Area of Tangent-Chord Triangle · Hard · Numerical value
  29. 31 Aug 2021, Shift 2 · Q89Common Tangent to Circle and Conic · Medium · Numerical value
  30. 24 Feb 2021, Shift 1 · Q74Focus-Directrix Form Extraction · Medium · Single correct
  31. 24 Feb 2021, Shift 1 · Q88Condition for a Circle · Medium · Numerical value
  32. 24 Feb 2021, Shift 2 · Q64Tangent to General Conic (T=0) · Easy · Single correct
  33. 24 Feb 2021, Shift 2 · Q82Locus of Constant Tangent Ratio · Medium · Numerical value
  34. 25 Feb 2021, Shift 1 · Q71Condition for Line Tangency · Medium · Single correct
  35. 25 Feb 2021, Shift 1 · Q89Condition for a Hyperbola · Medium · Numerical value
  36. 25 Feb 2021, Shift 2 · Q70Homogenization of curves · Hard · Single correct
  37. 25 Feb 2021, Shift 2 · Q71Shortest Distance via Common Normal · Medium · Single correct
  38. 25 Feb 2021, Shift 2 · Q72Coordinates of foci · Medium · Single correct
  39. 25 Feb 2021, Shift 2 · Q89Common Tangent to Circle and Conic · Hard · Numerical value
  40. 26 Feb 2021, Shift 1 · Q66Secant-Tangent Power Theorem · Medium · Single correct · has a figure
  41. 26 Feb 2021, Shift 2 · Q70Maximum and Minimum Distance to a Circle · Medium · Single correct
  42. 26 Feb 2021, Shift 2 · Q78Open the question · Easy · Single correct
  43. 26 Feb 2021, Shift 2 · Q90Common Tangent to Circle and Conic · Hard · Numerical value
  44. 22 Jul 2021, Shift 2 · Q67Similarity of Ellipses · Medium · Single correct
  45. 22 Jul 2021, Shift 2 · Q68Condition for Line to be Tangent · Medium · Single correct
  46. 22 Jul 2021, Shift 2 · Q71Point position relative to circle · Medium · Single correct
  47. 25 Jul 2021, Shift 1 · Q61Eccentricity calculation · Hard · Single correct
  48. 25 Jul 2021, Shift 1 · Q68Open the question · Medium · Single correct
  49. 25 Jul 2021, Shift 1 · Q75Open the question · Hard · Single correct
  50. 25 Jul 2021, Shift 2 · Q76Coordinates of foci · Hard · Single correct
  51. 25 Jul 2021, Shift 2 · Q81Vertex of a General Parabola · Medium · Numerical value
  52. 16 Mar 2021, Shift 2 · Q62Tangent Parallel or Perpendicular to a Line · Medium · Single correct
  53. 16 Mar 2021, Shift 2 · Q65Open the question · Medium · Single correct
  54. 16 Mar 2021, Shift 2 · Q66Open the question · Medium · Single correct
  55. 17 Mar 2021, Shift 1 · Q74Normal Passes Through Center · Medium · Single correct
  56. 17 Mar 2021, Shift 1 · Q75Number of Common Tangents · Medium · Single correct
  57. 17 Mar 2021, Shift 1 · Q86Number of Common Tangents · Easy · Numerical value
  58. 17 Mar 2021, Shift 2 · Q73Incenter via Equidistance · Medium · Single correct
  59. 17 Mar 2021, Shift 2 · Q78Area of Tangent-Chord Triangle · Medium · Single correct
  60. 17 Mar 2021, Shift 2 · Q80Condition for Line Tangency · Medium · Single correct
  61. 18 Mar 2021, Shift 1 · Q75Number of Common Tangents · Easy · Single correct
  62. 18 Mar 2021, Shift 1 · Q76Open the question · Easy · Single correct
  63. 18 Mar 2021, Shift 1 · Q84Open the question · Hard · Numerical value
  64. 18 Mar 2021, Shift 2 · Q74Open the question · Hard · Single correct
  65. 18 Mar 2021, Shift 2 · Q79Open the question · Hard · Single correct

JEE Main 202028 questions

  1. 8 Jan 2020, Shift 1 · Q63Open the question · Medium · Single correct
  2. 8 Jan 2020, Shift 1 · Q64Ellipse Normal Point Form · Medium · Single correct
  3. 8 Jan 2020, Shift 2 · Q64Condition of tangency · Medium · Single correct
  4. 8 Jan 2020, Shift 2 · Q65Hyperbola Normal Point Form · Medium · Single correct
  5. 8 Jan 2020, Shift 2 · Q74Tangent to General Conic (T=0) · Medium · Numerical value
  6. 9 Jan 2020, Shift 1 · Q65Condition of tangency · Medium · Single correct
  7. 9 Jan 2020, Shift 1 · Q66Eccentricity calculation · Easy · Single correct
  8. 9 Jan 2020, Shift 2 · Q65Eccentricity calculation · Medium · Single correct
  9. 9 Jan 2020, Shift 2 · Q66Parameter relation t1*t2 = -1 · Medium · Single correct
  10. 9 Jan 2020, Shift 2 · Q73Number of Common Tangents · Medium · Numerical value
  11. 2 Sep 2020, Shift 1 · Q65Open the question · Medium · Single correct
  12. 2 Sep 2020, Shift 1 · Q74Condition of tangency · Medium · Numerical value
  13. 2 Sep 2020, Shift 2 · Q65Open the question · Medium · Single correct
  14. 2 Sep 2020, Shift 2 · Q66Eccentricity calculation · Medium · Single correct
  15. 3 Sep 2020, Shift 1 · Q63Open the question · Medium · Single correct
  16. 3 Sep 2020, Shift 1 · Q64Open the question · Medium · Single correct
  17. 3 Sep 2020, Shift 1 · Q75Condition of tangency · Medium · Numerical value
  18. 3 Sep 2020, Shift 2 · Q64Length of Common Chord via Radical Axis · Medium · Single correct
  19. 3 Sep 2020, Shift 2 · Q65Distance Between Foci · Medium · Single correct
  20. 4 Sep 2020, Shift 1 · Q65Length of Latus Rectum · Medium · Single correct
  21. 4 Sep 2020, Shift 1 · Q66Hyperbola Normal Point Form · Medium · Single correct
  22. 4 Sep 2020, Shift 2 · Q65Radical axis of two circles · Medium · Single correct
  23. 4 Sep 2020, Shift 2 · Q66Ellipse Normal Point Form · Medium · Single correct
  24. 4 Sep 2020, Shift 2 · Q74Perpendicular distance from point · Hard · Numerical value
  25. 5 Sep 2020, Shift 1 · Q64Condition of tangency · Medium · Single correct
  26. 5 Sep 2020, Shift 1 · Q65Focal distance property · Easy · Single correct
  27. 6 Sep 2020, Shift 2 · Q65Family of Circles Touching a Line · Hard · Single correct
  28. 6 Sep 2020, Shift 2 · Q66Eccentricity when Normal at LR End Passes Through Minor Axis · Medium · Single correct

JEE Main 20172 questions

  1. 2 Apr 2017 (offline) · Q80Ellipse Normal Point Form · Medium · Single correct
  2. 2 Apr 2017 (offline) · Q81Open the question · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

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