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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceSingle correctEasyMulti-step

JEE Main 6 April 2023, Shift 2, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is α\alpha and the number of persons who speak only Hindi is β\beta, then the eccentricity of the ellipse 25(β2x2+α2y2)=α2β225\left(\beta^2x^2+\alpha^2y^2\right)=\alpha^2\beta^2 is
  1. (1)11712\frac{\sqrt{117}}{12}
  2. (2)11912\frac{\sqrt{119}}{12}Official answer
  3. (3)12912\frac{\sqrt{129}}{12}
  4. (4)31512\frac{3\sqrt{15}}{12}

Official answer

Option 2

NTA final key.

Chapter
Conic Sections
Topic
Ellipse Eccentricity
Idea tested
Eccentricity calculation

Same idea in other shifts

Asked 11× 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. 1 Feb 2024, Shift 1 · Q12For 0<θ<π/20<\theta<\pi/2, if the eccentricity of the hyperbola x2−y2cosec2θ=5x^2-y^2\mathrm{cosec}^2\theta=5 is 7\sqrt{7} times eccentricity of the…MediumSingle correct
  3. 1 Feb 2024, Shift 2 · Q13Let PP be a point on the ellipse x29+y24=1\frac{x^2}{9}+\frac{y^2}{4}=1. Let the line passing through PP and parallel to yy-axis meet the…HardSingle correct
  4. 25 Jul 2022, Shift 2 · Q12If the ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 meets the line x7+y26=1\frac{x}{7}+\frac{y}{2\sqrt{6}}=1 on the xx-axis and the line…EasySingle correct
  5. 27 Jun 2022, Shift 1 · Q13Let the eccentricity of an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>ba>b, be 14\frac{1}{4}. If this ellipse passes through the point…EasySingle correct
  6. 30 Jun 2022, Shift 1 · Q15Let the eccentricity of the ellipse x2+a2y2=25a2x^2 + a^2y^2 = 25a^2 be b times the eccentricity of the hyperbola x2−a2y2=5x^2 - a^2y^2 = 5, where a is the…HardSingle correct
  7. 25 Jul 2021, Shift 1 · Q61Let 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…HardSingle correct
  8. 9 Jan 2020, Shift 1 · Q66If e1\mathrm{e}_1 and e2\mathrm{e}_2 are the eccentricities of the ellipse, x218+y24=1\frac{x^2}{18}+\frac{y^2}{4}=1 and the hyperbola,…EasySingle 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.