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 a and the number of persons who speak only Hindi is b, then the eccentricity of the ellipse 25(β2 x2 + α2 y2) = α2 β2 is
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 a and the number of persons who speak only Hindi is b, then the eccentricity of the ellipse 25(β2 x2 + α2 y2) = α2 β2 is
Updated On: Mar 21, 2025
- \(\frac{117}{12}\)
- \(\frac{119}{12}\)
- \(\frac{129}{12}\)
- \(3\frac{15}{12}\)
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The Correct Option is B
Solution and Explanation
We are given the number of persons who speak only English as \(\alpha = 60\), and only Hindi as \(\beta = 25\). The eccentricity of the ellipse is given by:
\[
e^2 = 1 - \frac{25 \times 25}{60^2} = \frac{119}{144}
\]
Thus,
\[
e = \frac{\sqrt{119}}{12}
\]
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