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KVPY2011MathematicsSequences and Series

Consider an incomplete pyramid of balls on a square base having 18 layers; and having 13 balls on each side of the top layer. Then the total number N of balls in that pyramid satisfies.

Options

  1. A9000 < N < 10000
  2. B8000 < N < 9000
  3. C7000 < N < 8000
  4. D10000 < N < 12000

Correct answer

B. 8000 < N < 9000

Step-by-step solution

Top layer has (13 13) balls similarly are layer below top layer will have (14 14) balls We have 18 layer So total number of balls array l N =(13)²+(14)²+ . .+(30)² ~N = 30 31 61 6 - 12 13 25 6 ~N =8805 array

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