JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q75

Question 75 of 90 in this shift, Maths question 15 of 30, Section A.

If the tangent to the curve

y = x^3

at the point

P(t, t^3)

meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio

1 : 2

is :

(1) $0$
(2) $2t^3$
(3) $-t^3$
(4) $-2t^3$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Application of Derivatives
Topic: Tangents and Normals
Idea tested: Tangent Intersecting Curve Again

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.