jee-main 2012 Q75

jee-main · India · 26may Measures of Location and Spread
Statement 1: The variance of first $n$ odd natural numbers is $\frac { n ^ { 2 } - 1 } { 3 }$ Statement 2: The sum of first $n$ odd natural numbers is $n ^ { 2 }$ and the sum of squares of first $n$ odd natural numbers is $\frac { n \left( 4 n ^ { 2 } + 1 \right) } { 3 }$.
(1) Statement 1 is true, Statement 2 is false.
(2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
(3) Statement 1 is false, Statement 2 is true.
(4) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
Statement 1: The variance of first $n$ odd natural numbers is $\frac { n ^ { 2 } - 1 } { 3 }$\\
Statement 2: The sum of first $n$ odd natural numbers is $n ^ { 2 }$ and the sum of squares of first $n$ odd natural numbers is $\frac { n \left( 4 n ^ { 2 } + 1 \right) } { 3 }$.\\
(1) Statement 1 is true, Statement 2 is false.\\
(2) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.\\
(3) Statement 1 is false, Statement 2 is true.\\
(4) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.