JEE Main20205 Sep 2020Evening ShiftMathematicsStatisticsActual

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:

Options

Ax 2 - 10 x + 18 = 0
B2 x 2 - 20 x + 19 = 0
Cx 2 - 10 x + 19 = 0
Dx 2 - 20 x + 18 = 0

Correct answer

C. x 2 - 10 x + 19 = 0

Step-by-step solution

5 + 3 + 7 + a + b = 25 ⇒ a + b = 10 S.D. = 5 2 + 3 2 + 7 2 + a 2 + b 2 5 - 5 2 = 2 = a 2 + b 2 + 83 5 - 25 = 4 ⇒ a 2 + b 2 = 62 ⇒ ( a + b ) 2 - 2 a b = 62 ⇒ a b = 19 so equation whose roots are a and b is x 2 - 10 x + 19 = 0

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