JEE Main 2025 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 2 April 2025, Shift 2, Maths Q12

Question 12 of 75 in this shift, Maths question 12 of 25, Section A.

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

(1) $\frac{3}{\sqrt{19}}$
(2) $\frac{4}{\sqrt{17}}$ Official answer
(3) $\frac{\sqrt{5}}{7}$
(4) $\frac{\sqrt{3}}{16}$

Official answer

Option 2

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Distance Between Foci

Same topic in other shifts

All Ellipse Eccentricity questions

2 Apr 2026, Shift 1 · Q10Let an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a<b$ , pass through the point $(4, 3)$ and have eccentricity $\frac{\sqrt5}{3}$ . Then…MediumSingle correct
4 Apr 2026, Shift 1 · Q22Consider the parabola $P: y^2=4kx$ and the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ . Let the line segment joining the points of…MediumNumerical value
5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $S(4, 0)$ and its eccentricity be $\frac{4}{5}$ . If the point…EasySingle correct
8 Apr 2026, Shift 2 · Q2The number of values of $z \in \mathbb{C}$ , satisfying the equations $|z - (4 + 8i)| = \sqrt{10}$ and…HardSingle correct
2 Apr 2025, Shift 1 · Q4If S and S' are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and P be a point on the ellipse, then…MediumSingle correct
3 Apr 2025, Shift 2 · Q12Let $C$ be the circle of minimum area enclosing the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with eccentricity $\frac{1}{2}$ and…HardSingle 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.