JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

If 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 curve :

(1) $x^2+\frac{y^2}{81}=2$
(2) $\frac{y^2}{9}-x^2=8$
(3) $y=4x^2+5$
(4) $\frac{x}{3}-y^2=2$ Official answer

Official answer

Option 4

NTA final key (2022 Session 1).

Chapter: Application of Derivatives
Topic: Tangents and Normals
Idea tested: Tangents Passing Through Origin

Same topic in other shifts

All Tangents and Normals questions

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
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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.