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UPSC NDA 2 2012 Mathematics Paper
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© examsnet.com
Question : 3
Total: 120
Consider the following statements :
1. The sum of cubes of first 20 natural numbers is 44400.
2. The sum of squares of first 20 natural numbers is 2870.
Which of the above statements is/are correct?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
∵
1
3
+
2
3
+
3
3
+
.
.
.
.
.
.
+
n
3
=
(
n
(
n
+
1
)
2
)
2
∴
1
1
3
+
2
3
+
3
3
+
.
.
.
.
.
.
+
20
3
=
(
20.21
2
)
2
=
(
10
×
21
)
2
=
44100
1
2
+
2
2
+
3
3
+
.
.
.
.
.
.
+
n
2
=
1
6
n
(
n
+
1
)
(
2
n
+
1
)
∴
1
2
+
2
2
+
.
.
.
.
.
.
+
20
2
=
1
6
20.21
.41
=
2870
© examsnet.com
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