Question

The remainder obtained when the sum of squares first n odd natural numbers is divided the sum of squares of first n even natural numbers is

• A. 1
• B. 0
• C. 79
• D. 89

Answer 1

The correct option is C

79

The sum of squares first n odd natural numbers = $\frac{n(2n-1)(2n+1)}{3}$ ------ (i)

The sum of squares first n even natural numbers = $\frac{2n(n+1)(2n+1)}{3}$ ------ (ii)

Ratio : $\frac{\left(i\right)}{\left(ii\right)}$ = $\frac{(2n+1)}{2(n+1)}$

Here n = 40 , then the remainder obtained when 79 is divided by 82 is 79.