JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let

x=2t

y=\frac{t^2}{3}

be a conic. Let S be the focus and B be the point on the axis of the conic such that

SA\perp BA

, where A is any point on the conic. If k is the ordinate of the centroid of the

\Delta SAB

, then

\lim_{t\to1}k

is equal to :

(1) $\frac{17}{18}$
(2) $\frac{19}{18}$
(3) $\frac{11}{18}$
(4) $\frac{13}{18}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Focus-Directrix Form Extraction

Same idea in other shifts

Asked 4× in all

7 Apr 2025, Shift 1 · Q10Let P be the parabola, whose focus is $(-2, 1)$ and directrix is $2x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose…MediumSingle correct
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24 Feb 2021, Shift 1 · Q74The locus of the mid-point of the line segment joining the focus of the parabola $y^2 = 4ax$ to a moving point of the parabola, is another…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 108 of the 174 JEE Main shifts held from 2017 to 2026.