Group of 100 persons 75 speak English and 40 speak | Sets

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JEE MAIN 2023

08-04-2023 S2

Question

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 $25\left(\beta^2 x^2+\alpha^2 y^2\right)=\alpha^2 \beta^2$ is

Select the correct option:

A

$\frac{3 \sqrt{15}}{12}$

B

$\frac{\sqrt{117}}{12}$

C

$\frac{\sqrt{119}}{12}$

D

$\frac{\sqrt{129}}{12}$

✓ Correct! Well done.

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Solution

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