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Friday, 9 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q61

Question 61 of 90 in this shift, Maths question 1 of 30, Section A.

Let an ellipse E:x2a2+y2b2=1E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a2>b2a^2>b^2, passes through (32,1)\left(\sqrt{\frac{3}{2}},1\right) and has eccentricity 13\frac{1}{\sqrt3}. If a circle, centered at focus F(α,0)F(\alpha,0), α>0\alpha>0, of E and radius 23\frac{2}{\sqrt3}, intersects E at two points P and Q, then PQ2PQ^2 is equal to :
  1. (1)83\frac{8}{3}
  2. (2)43\frac{4}{3}
  3. (3)163\frac{16}{3}Official answer
  4. (4)33

Official answer

Option 3

NTA final key.

Chapter
Conic Sections
Topic
Ellipse Eccentricity
Idea tested
Eccentricity calculation

Same idea in other shifts

Asked 3× in all
  1. 5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 be S(4,0)S(4, 0) and its eccentricity be 45\frac{4}{5}. If the point…EasySingle correct
  2. 9 Jan 2020, Shift 2 · Q65The length of the minor axis (along yy-axis) of an ellipse in the standard form is 43\frac{4}{\sqrt3}. If this ellipse touches the line,…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.