Learn

Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Equation of Normal

JEE Main asked Equation of Normal 6 times in 6 of the 108 shifts Lumi analysed, in 2017, 2020 and 2021. It belongs to Tangents and Normals, in Application of Derivatives (Maths). The longest wait between two years asking it was 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2020 and 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
3 of 8
First asked
2017
last in 2021
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 2020 and 2021. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.510.86’170.25’200.07’210’220’230’240’250’26

Raw count: 2017: 1 in 1 shift · 2020: 3 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20212 of 24
  • 20203 of 12
  • 20171 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Normal to curve at axis intercept passes through point
  • Normal at point nearest to line

Difficulty

Easy 1Medium 5Hard 0

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 26 Feb 2021, Shift 2 · Q83Let the normals at all the points on a given curve pass through a fixed point (a,b)(a, b). If the curve passes through (3,−3)(3, -3) and…MediumNumerical value
  2. 4 Aug 2021, Shift 1 · Q68The equation of the normal to the curve y=e−∣x∣y=e^{-|x|} at a point, where the curve cuts the line x=−1x=-1 isEasySingle correct
  3. 2 Sep 2020, Shift 2 · Q60The equation of the normal to the curve y=(1+x)2y+cos⁡2(sin⁡−1x)y=(1+x)^{2y}+\cos^2(\sin^{-1}x) at x=0x=0 is :MediumSingle correct
  4. 2 Sep 2020, Shift 1 · Q64Let P(h, k) be a point on the curve y=x2+7x+2y=x^{2}+7x+2, nearest to the line, y=3x−3y=3x-3. Then the equation of the normal to the curve at P is :MediumSingle correct
  5. 8 Jan 2020, Shift 2 · Q60The length of the perpendicular from the origin, on the normal to the curve, x2+2xy−3y2=0x^2 + 2xy - 3y^2 = 0 at the point (2,2)(2, 2) is :MediumSingle correct
  6. 2 Apr 2017 (offline) · Q72The normal to the curve y(x−2)(x−3)=x+6y(x-2)(x-3)=x+6 at the point where the curve intersects the yy-axis passes through the point :MediumSingle correct

Shifts: 2 Apr 2017 (offline), 8 Jan 2020, Shift 2, 2 Sep 2020, Shift 2, 2 Sep 2020, Shift 1, 26 Feb 2021, Shift 2, 4 Aug 2021, Shift 1.

Same topic

Other ideas in Tangents and Normals

Tangents and Normals has 20 ideas JEE Main has asked; 7 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas