JEE MAIN - Mathematics (2020 - 5th September Evening Slot - No. 1)
If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :
data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :
x2 – 20x + 18 = 0
2x2 – 20x + 19 = 0
x2 – 10x + 18 = 0
x2 – 10x + 19 = 0
Explanation
Mean = $${{3 + 5 + 7 + a + b} \over 5}$$ = 5
$$ \Rightarrow $$ $$a$$ + b = 10
Variance = $${{{3^2} + {5^2} + {7^2} + {a^2} + {b^2}} \over 5}$$ - (5)2 = 4
$$ \Rightarrow $$ $${{a^2} + {b^2}}$$ = 62
$$ \Rightarrow $$ $${\left( {a + b} \right)^2} - 2ab$$ = 62
$$ \Rightarrow $$ $$ab$$ = 19
So $$a$$ and b are the roots of the equation
x2 – 10x + 19 = 0
$$ \Rightarrow $$ $$a$$ + b = 10
Variance = $${{{3^2} + {5^2} + {7^2} + {a^2} + {b^2}} \over 5}$$ - (5)2 = 4
$$ \Rightarrow $$ $${{a^2} + {b^2}}$$ = 62
$$ \Rightarrow $$ $${\left( {a + b} \right)^2} - 2ab$$ = 62
$$ \Rightarrow $$ $$ab$$ = 19
So $$a$$ and b are the roots of the equation
x2 – 10x + 19 = 0
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