In a group of 100 persons, 75 speak English and 40 speak Hindi. E… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 6 April, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

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 $\alpha$ and the number of persons who speak only Hindi is $\beta$ , then the eccentricity of the ellipse $25\left(\beta^2 x^2 + \alpha^2 y^2 \right) = \alpha \beta^2$ is:

A
$\frac{\sqrt{129}}{12}$
B
$\frac{\sqrt{117}}{12}$
C
$\frac{\sqrt{119}}{12}$
D
$\frac{3\sqrt{15}}{12}$

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