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Question:

Statement 1: The variance of first n even natural numbers is n²/4
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

Statement 1 is true, Statement 2 is false.

Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1

Statement 1 is false, Statement 2 is true

Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1

Solution:

Sum of first n even natural numbers=2+4+6+...+2n=2(1+2+...+n)=2n(n+1)2=n(n+1)