JEE Main Maths · Application of Derivatives

Tangents and Normals in JEE Main

Name: Tangents and Normals: JEE Main previous year questions
Creator: Lumi

Tangents and Normals (Maths, Application of Derivatives) came 7 times in 6 of the 42 JEE Main shifts Lumi analysed, across 5 distinct ideas. 0 of them came in 2024–26; it was last asked in 2023.

Questions: 7; in 6 shifts
Ideas asked: 5; 2 asked more than once
Numerical answer: 2; 29% of its questions
Pattern: Asked most years; rarely asked since 2024

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 7Hard 0

Format

Single correct5 Q
Numerical value2 Q

Ideas inside the topic

5 ideas

Tangents to Implicit Curves2 Q
Equation of Normal2 Q
Finding Curve from Tangent/Normal Properties1 Q
Equation of Tangent1 Q
Tangents Passing Through Origin1 Q

Where it sits

Part of Application of Derivatives, which had 47 questions in all. Tangents and Normals accounts for 15% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Conic Sections, Differential Equations.

Every question

All 7 Tangents and Normals questions

Newest first, each with its options and official answer.

6 Apr 2023, Shift 1 · Q28Let the tangent to the curve $x^2+2x-4y+9=0$ at the point $P(1,3)$ on it meet the $y$ -axis at A. Let the line passing through P and…MediumNumerical value
24 Jun 2022, Shift 1 · Q11If the tangent at the point $(x_1, y_1)$ on the curve $y=x^3+3x^2+5$ passes through the origin, then $(x_1, y_1)$ does NOT lie on the…MediumSingle correct
3 Aug 2021, Shift 2 · Q73A curve passes through the point $(-1, 4)$ . If the normal to it at any point $(x, y)$ on it passes through $(2, 0)$ , then its equation isMediumSingle correct
8 Jan 2020, Shift 1 · Q74Let the normal at a point P on the curve $y^2-3x^2+y+10=0$ intersect the $y$ -axis at $\left(0,\frac{3}{2}\right)$ . If m is the slope of…MediumNumerical value
2 Sep 2020, Shift 1 · Q60If the tangent to the curve $y=x+\sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and…MediumSingle correct
2 Sep 2020, Shift 1 · Q64Let P(h, k) be a point on the curve $y=x^{2}+7x+2$ , nearest to the line, $y=3x-3$ . Then the equation of the normal to the curve at P is :MediumSingle correct
2 Apr 2017 (offline) · Q72The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the $y$ -axis passes through the point :MediumSingle correct