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Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If x y = 55 42 , then what is the value of n ?

Options

  1. A24
  2. B25
  3. C27
  4. D30

Correct answer

C. 27

Step-by-step solution

Mean of squares of first n natural number x= n(n+1)(2 n+1) 6 n = (n+1)(2 n+1) 6 Square of mean of first n natural numbers aligned & y= ( n(n+1) 2 n )^2= (n+1)^2 4 & x y = 2(2 n+1) 3(n+1) = 55 42 & 28(2 n+1)=55(n+1) n=27 aligned

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