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

5 Apr 2024, Shift 2 · Q27Let a line perpendicular to the line $2x-y=10$ touch the parabola $y^2=4(x-9)$ at the point $P$ . The distance of the point $P$ from the…MediumNumerical value
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
10 Apr 2023, Shift 2 · Q25Let the quadratic curve passing through the point $(-1, 0)$ and touching the line $y = x$ at $(1, 1)$ be $y = f(x)$ . Then the…MediumNumerical value
25 Jul 2022, Shift 2 · Q29Let the area enclosed by the $x$ -axis, and the tangent and normal drawn to the curve $4x^3-3xy^2+6x^2-5xy-8y^2+9x+14=0$ at the point…HardNumerical value
26 Jul 2022, Shift 2 · Q12The equation of a common tangent to the parabolas $y=x^2$ and $y=-(x-2)^2$ isMediumSingle correct
27 Jul 2022, Shift 1 · Q26Let $M$ and $N$ be the number of points on the curve $y^5 - 9xy + 2x = 0$ , where the tangents to the curve are parallel to $x$ -axis and…MediumNumerical value

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 108 of the 174 JEE Main shifts held from 2017 to 2026.