QJEEM21Ma1172: JEE Main 2021 Mathematics - Class 11 JEEM21Ma1172 Solution: Let the mean and variance of four numbers 3, 7, x and y(x > y)…

Question

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Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x

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y is ______________.

Accepted Answer

5 = {{3 + 7 + x + y} \over 4} \Rightarrow x + y = 10

Var(x) =

10 = {{{3^2} + {7^2} + {x^2} + {y^2}} \over 4} - 25

140 = 49 + 9 + {x^2} + {y^2}

{x^2} + {y^2} = 82

x + y = 10

\Rightarrow

(x, y) = (9, 1)

Four numbers are 21, 9, 10, 8

Mean =

{{48} \over 4}

= 12

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