Statement-1 : The variance of first n even natural numbers is n^2 - 1 4 Statement-2 : The sum of first n natural numbers is n(n+1) 2 and the sum of squares of first n natural numbers is n(n+1)(2n+1) 6

JEE Main 2009 Mathematics question

Statement-1 : The variance of first n even natural numbers is Statement-2 : The sum of first natural numbers is and the sum of squares of first n natural numbers is

(1)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
(2)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
(3)Statement-1 is true, Statement-2 is false
(4)Statement-1 is false, Statement-2 is trueCorrect

Answer: (4)

Solution

The first n even numbers are 2 × (1, 2, …, n). Variance of 1, …, n is , so the variance of the even numbers is

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Question ID VK-039182