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Question

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

A
9000<N<10000
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B
8000<N<9000
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C
7000<N<8000
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D
10000<N<12000
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Solution

The correct option is B 8000<N<9000

The top layer has (13×13) balls the layer below it will have (14×14) balls

We have 18 layers

So the total number of balls

N=(13×13)+(14×14)+.......(30×30)N=132+142+.....302

Sum of squares of first n natural numbers is n(n+1)(2n+1)6

N= sum of first 30 sum of first 12

N=30×31×61612×13×256N=8805

8000<N<9000

Hence, option B is correct.

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