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JEE Main20236 Apr 2023Evening ShiftMathematicsSets and RelationsActual

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 and the number of persons who speaks only Hindi is β , then the eccentricity of the ellipse 25 β 2 x 2 + α 2 y 2 = α 2 β 2 is

Options

  1. A119 12
  2. B117 12
  3. C3 15 12
  4. D129 12

Correct answer

A. 119 12

Step-by-step solution

Given, In a group of 100 persons 75 speak English and 40 speak Hindi, And each person speaks at least one of the two languages, And the number of persons who speak only English is α and the number of persons who speaks only Hindi is β , Now from above diagram we can see that, β = 100 - 75 = 25 So, α = 75 - 40 - 25 = 60 Hence, number of people who speak English only is α = 60 and Hindi is β = 25 , Now putting the value in given equation of ellipse we get, 25 x 2 60 2 + y 2 25 2 = 1 &#86

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