If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16 , then the value of m + n is equal to

Question

If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16 , then the value of m + n is equal to,

MARKS App · Accepted Answer

v a r 1 , 2 , … n = 10 ⇒ 1 2 + 2 2 + … + n 2 n - 1 + 2 + … + n n 2 = 10 ⇒ n + 1 2 n + 1 6 - n + 1 2 2 = 10 ⇒ n 2 - 1 = 120 ⇒ n = 11 v a r 2 , 4 , 6 … . , 2 m = 16 ⇒ v a r 1 , 2 … . , m = 4 ⇒ m 2 - 1 = 48 ⇒ m = 7 ⇒ m + n = 18

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