JEE MAIN - Mathematics (2021 - 26th August Evening Shift - No. 22)
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 $$-$$ y is ______________.
Answer
12
Explanation
$$5 = {{3 + 7 + x + y} \over 4} \Rightarrow x + y = 10$$
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
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
Comments (0)
