Statement-2 is true Statement-1: Sum of n even natural numbers =n(n+1) Mean (xˉ)=nn(n+1)=n+1 Variance =[n1∑(x1)2]−(xˉ)2=n1[22+42+….+(2n)2]−(n+1)2=n122[12+22+….+n2]−(n+1)2=n46n(n+1)(2n+1)−(n+1)2=3(n+1)[2(2n+1)−3(n+1)]=3(n+1)[4n+2−3n−3]=3(n+1)(n−1)=3n2−1 ∴ Statement 1 is false.
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…
JEE Main 2009 — Mathematics Probability & Statistics
2009mcqeasy
Statement-1 : The variance of first n even natural numbers is 4n2−1 Statement-2 : The sum of first n natural numbers is 2n(n+1) and the sum of squares of first n natural numbers is 6n(n+1)(2n+1)
Official previous-year question
Held on 30 Apr 2009 · Verified 6 Jul 2026.
Options
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
- C
Statement-1 is true, Statement-2 is false
- D
Statement-1 is false, Statement-2 is true
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