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NDA 2 2024 Maths, question 102

Topic: Statistics

Q102

The mean of nn observations 1,4,9,16,…,n21,4,9,16,\ldots ,n^{2} is 130130. What is the value of nn?

  1. (a) 1818
  2. (b) 1919Correct answer
  3. (c) 2020
  4. (d) 2121

Solution.

Answer: (b) 1919

  1. The mean of 1² through n² is (n+1)(2n+1)/6.
  2. Set this to 130, giving 2n²+3n−779=0=(n−19)(2n+41).
  3. The positive integer solution is n=19, checked by 20×39/6=130.