KVPY SA Exam 2011 Question Paper

Question : 11 of 80

Marks: +1, -0

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

9000 < N < 10000
8000 < N < 9000
7000 < N < 8000
10000 < N < 12000

Validate

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
N

= (13)^2 + (14)^2 + ........ + (30)^2

N={30×31×61}/6-{12×13×25}/6

= 8805.

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