JEE Main · Maths · Application of Derivatives
Tangents and Normals: JEE Main previous year questions
36 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Gone quiet. 1 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 36
- in 30 of 108 shifts
- Years asked
- 6/8
- last asked 2024
- Since 2024
- Quiet
- 1 question in 2024–26
- Weighted estimate
- –
- history: 0.3 a shift on average, typically 0.0–0.5
Key findings
- 01
Asked in 6 of 8 years with analysed shifts and in 30 of 108 shifts: 36 questions, #95 of 196 topics. The years that asked it were 1.4 apart on average. Last asked in 2024.
- 02
74% of its questions since 2020 tested an idea no earlier year had asked; 6 repeated an idea from the year before.
- 03
The most repeated idea is Equation of Normal, asked 6 times in 6 shifts (2017, 2020, 2021), most often as “normal to curve at axis intercept passes through point”.
- 04
JEE Main has asked 20 of the 63 ideas in this topic; 37 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (64%); 36% need a numerical answer, 6% are easy and 8% hard. It went down from 0.5 to 0.0 questions a shift since 2024.
- 06
The skill tested most is multi-step (86%), then calculation (8%).
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: 6 in 12 shifts · 2021: 15 in 24 shifts · 2022: 11 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
- 0.5
- a shift, of 25
- Since 2024
- 0.0
- -0.5
- Usual gap
- 1.4 yrs
- between years asking it
- Shifts with it
- 30/108
- 28% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 36 questions on Tangents and Normals since 2017.
Difficulty
QUESTIONS- Easy2 · 6%
- Medium31 · 86%
- Hard3 · 8%
Format
SHARE- Single correct · 23 Q64%
- Numerical value · 13 Q36%
Skill tested
SHARE- Multi-step · 31 Q86%
- Calculation · 3 Q8%
- Application · 2 Q6%
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.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 20 of the 63 ideas in this topic. 37 have never been asked yet.
- Asked directly20 · 32%
- Touched inside another question6 · 10%
- Never asked37 · 59%
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.
15 ideas inside
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
20 different ideas were tested; 7 came more than once.
normal to curve at axis intercept passes through point
Single correct · 6 shifts · 1 numericalline tangent to two curves
Numerical value · 4 shifts · 2 numericaltangent, parallel line and distance between points
Single correct · 3 shifts · 1 numericalintercept of normal to fitted curve
Numerical value · 3 shifts · 2 numericaltangent to implicit curve parallel to given line
Single correct · 3 shifts · 1 numericalangle of intersection of two curves
Single correct · 2 shiftsorthogonal curves condition
Numerical value · 2 shifts · 1 numericalpoint of contact of tangent perpendicular to line
Numerical value · 1 shift · 1 numericalarea enclosed by tangent, normal and axis
Numerical value · 1 shift · 1 numericalslope of line from tangent to parabola
Single correct · 1 shiftarea of triangle from normal
Numerical value · 1 shift · 1 numericalcount points with tangent parallel to axes
Numerical value · 1 shift · 1 numericalpoint where tangent passes through origin
Single correct · 1 shifttangent slope on parametric curve
Single correct · 1 shiftsum of intercepts made by tangent
Single correct · 1 shiftcurve from normal passing through fixed point
Single correct · 1 shiftminimum area of triangle cut by tangent to ellipse
Numerical value · 1 shift · 1 numericalshortest distance between line and curve
Single correct · 1 shifttangent meeting curve again, section point
Single correct · 1 shifttangent to modulus-integral curve with given slope
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Equation of Normalnormal to curve at axis intercept passes through point | 6 | 6 | Single correctMulti-step | 1 | |
| Common Tangents to Two Curvesline tangent to two curves | 4 | 4 | Numerical valueMulti-step | 2 | |
| Equation of Tangenttangent, parallel line and distance between points | 3 | 3 | Single correctMulti-step | 1 | |
| Intercepts of Tangent and Normalintercept of normal to fitted curve | 3 | 3 | Numerical valueMulti-step | 2 | |
| Tangents to Implicit Curvestangent to implicit curve parallel to given line | 3 | 3 | Single correctMulti-step | 1 | |
| Angle Between Curvesangle of intersection of two curves | 2 | 2 | Single correctCalculation | – | |
| Orthogonal Intersection of Curvesorthogonal curves condition | 2 | 2 | Numerical valueCalculation | 1 | |
| Point of Tangency from Given Slopepoint of contact of tangent perpendicular to line | 1 | 1 | Numerical valueMulti-step | 1 | |
| Area of Triangle Formed by Tangent and Normalarea enclosed by tangent, normal and axis | 1 | 1 | Numerical valueMulti-step | 1 | |
| Condition for a Line to Touch a Curveslope of line from tangent to parabola | 1 | 1 | Single correctMulti-step | – | |
| Normals Passing Through a Given Pointarea of triangle from normal | 1 | 1 | Numerical valueMulti-step | 1 | |
| Tangents Parallel to Coordinate Axescount points with tangent parallel to axes | 1 | 1 | Numerical valueMulti-step | 1 | |
| Tangents Passing Through Originpoint where tangent passes through origin | 1 | 1 | Single correctMulti-step | – | |
| Tangents to Parametric Curvestangent slope on parametric curve | 1 | 1 | Single correctMulti-step | – | |
| Constant Sum of Interceptssum of intercepts made by tangent | 1 | 1 | Single correctApplication | – | |
| Finding Curve from Tangent/Normal Propertiescurve from normal passing through fixed point | 1 | 1 | Single correctMulti-step | – | |
| Optimizing Tangent-Bounded Areaminimum area of triangle cut by tangent to ellipse | 1 | 1 | Numerical valueMulti-step | 1 | |
| Shortest Distance via Common Normalshortest distance between line and curve | 1 | 1 | Single correctMulti-step | – | |
| Tangent Intersecting Curve Againtangent meeting curve again, section point | 1 | 1 | Single correctMulti-step | – | |
| Tangents to Piecewise/Modulus Functionstangent to modulus-integral curve with given slope | 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
Tangents and Normals 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.
JEE Main 20241 question in 1 shift
- 5 Apr, Shift 2Q27Let a line perpendicular to the line touch the parabola at the point . The distance of the point from the…
Idea: Point of Tangency from Given Slope
New ideaMediumNumerical value
JEE Main 20232 questions in 2 shifts
- 6 Apr, Shift 1Q28Let the tangent to the curve at the point on it meet the -axis at A. Let the line passing through P and…
Idea: Equation of Tangent
MediumNumerical value - 10 Apr, Shift 2Q25Let the quadratic curve passing through the point and touching the line at be . Then the…
Idea: Intercepts of Tangent and Normal
MediumNumerical value
JEE Main 202211 questions in 10 shifts
- 25 Jul, Shift 2Q29Let the area enclosed by the -axis, and the tangent and normal drawn to the curve at the point…
Idea: Area of Triangle Formed by Tangent and Normal
New ideaHardNumerical value - 26 Jul, Shift 2Q12The equation of a common tangent to the parabolas and is
Idea: Common Tangents to Two Curves
New ideaMediumSingle correct - 27 Jul, Shift 1Q26Let and be the number of points on the curve , where the tangents to the curve are parallel to -axis and…
Idea: Tangents Parallel to Coordinate Axes
New ideaMediumNumerical value - 27 Jul, Shift 2Q29A common tangent T to the curves and does not pass…
Idea: Common Tangents to Two Curves
New ideaHardNumerical value - 29 Jul, Shift 2Q27If the tangent to the curve at the point is also tangent to the curve at the point , then…
Idea: Common Tangents to Two Curves
New ideaMediumNumerical value - 24 Jun, Shift 1Q11If the tangent at the point on the curve passes through the origin, then does NOT lie on the…
Idea: Tangents Passing Through Origin
New ideaMediumSingle correct - 25 Jun, Shift 2Q14If the angle made by the tangent at the point on the curve , ,…
Idea: Tangents to Parametric Curves
New ideaMediumSingle correct - 25 Jun, Shift 2Q18If the line , , is the tangent to the parabola at the point and is the vertex of the parabola,…
Idea: Condition for a Line to Touch a Curve
New ideaMediumSingle correct - 26 Jun, Shift 1Q9Let S be the set of all natural numbers, for which the line is a tangent to the curve…
Idea: Tangents to Implicit Curves
MediumSingle correct - 26 Jun, Shift 2Q11If is the slope of a common tangent to the curves and , then is equal…
Idea: Common Tangents to Two Curves
New ideaMediumSingle correct - 28 Jun, Shift 1Q26Let be a line which is normal to the curve at a point P on the curve. If the point Q(6, 4) lies on the line and O is…
Idea: Normals Passing Through a Given Point
New ideaMediumNumerical value
JEE Main 202115 questions in 11 shifts
- 3 Aug, Shift 1Q67The sum of the intercepts on the coordinate axes made by the tangent at any point on the curve, is
Idea: Constant Sum of Intercepts
New ideaMediumSingle correct - 3 Aug, Shift 2Q73A curve passes through the point . If the normal to it at any point on it passes through , then its equation is
Idea: Finding Curve from Tangent/Normal Properties
New ideaMediumSingle correct - 4 Aug, Shift 1Q68The equation of the normal to the curve at a point, where the curve cuts the line is
Idea: Equation of Normal
Asked the year beforeEasySingle correct - 4 Aug, Shift 1Q70The equation of the tangent to the curve at the point whose abscissa is 1, is
Idea: Equation of Tangent
New ideaMediumSingle correct - 4 Aug, Shift 1Q75If the ellipse and the circle intersect at an angle , then a value of 'b' is
Idea: Angle Between Curves
New ideaHardSingle correct - 4 Aug, Shift 2Q68Equation of a tangent to the curve, which is parallel to the line, is
Idea: Tangents to Piecewise/Modulus Functions
New ideaMediumSingle correct - 4 Aug, Shift 2Q73If the area of the triangle formed by the tangent at a point in the first quadrant on the ellipse, and its axes is 4 sq.…
Idea: Intercepts of Tangent and Normal
Asked the year beforeMediumSingle correct - 27 Aug, Shift 1Q87If the minimum area of the triangle formed by a tangent to the ellipse and the co-ordinate axis is…
Idea: Optimizing Tangent-Bounded Area
New ideaMediumNumerical value - 31 Aug, Shift 2Q66An angle of intersection of the curves, and ,…
Idea: Angle Between Curves
New ideaMediumSingle correct - 24 Feb, Shift 1Q75If the tangent to the curve at the point meets the curve again at Q, then the ordinate of the point which divides PQ…
Idea: Tangent Intersecting Curve Again
New ideaMediumSingle correct - 24 Feb, Shift 2Q70If the curve , R, passes through the point (1, 2) and the tangent line to this curve at origin is , then the…
Idea: Equation of Tangent
New ideaEasySingle correct - 25 Feb, Shift 1Q72If the curves, and intersect each other at an angle of ,…
Idea: Orthogonal Intersection of Curves
New ideaMediumSingle correct - 25 Feb, Shift 2Q71The shortest distance between the line and the curve is :
Idea: Shortest Distance via Common Normal
New ideaMediumSingle correct - 25 Feb, Shift 2Q85If the curves and cut at right angles, then is equal to ________.
Idea: Orthogonal Intersection of Curves
New ideaMediumNumerical value - 26 Feb, Shift 2Q83Let the normals at all the points on a given curve pass through a fixed point . If the curve passes through and…
Idea: Equation of Normal
Asked the year beforeMediumNumerical value
JEE Main 20206 questions in 5 shifts
- 8 Jan, Shift 1Q74Let the normal at a point P on the curve intersect the -axis at . If m is the slope of…
Idea: Tangents to Implicit Curves
New ideaMediumNumerical value - 8 Jan, Shift 2Q60The length of the perpendicular from the origin, on the normal to the curve, at the point is :
Idea: Equation of Normal
Asked the year beforeMediumSingle correct - 2 Sep, Shift 1Q60If the tangent to the curve at a point is parallel to the line joining and…
Idea: Tangents to Implicit Curves
New ideaMediumSingle correct - 2 Sep, Shift 1Q64Let P(h, k) be a point on the curve , nearest to the line, . Then the equation of the normal to the curve at P is :
Idea: Equation of Normal
Asked the year beforeMediumSingle correct - 2 Sep, Shift 2Q60The equation of the normal to the curve at is :
Idea: Equation of Normal
Asked the year beforeMediumSingle correct - 3 Sep, Shift 2Q74If the tangent to the curve, at a point and the normal to the parabola, at the point intersect at…
Idea: Intercepts of Tangent and Normal
New ideaMediumNumerical value
JEE Main 20171 question in 1 shift
- 2 Apr (offline)Q72The normal to the curve at the point where the curve intersects the -axis passes through the point :
Idea: Equation of Normal
MediumSingle correct
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.