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KVPY SA Exam 2011 Question Paper
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© examsnet.com
Question : 11
Total: 80
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.
© examsnet.com
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