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Manipal Entrance Test 2014 Math Paper
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© examsnet.com
Question : 6
Total: 80
The variance of first n natural numbers is
n
(
n
+
1
)
12
(
n
+
1
)
(
n
+
5
)
12
(
n
+
1
)
(
n
−
5
)
12
(
n
)
(
n
−
5
)
12
Validate
Solution:
Variance of first n natural numbers is given by
Variance
=
∑
n
2
n
−
(
∑
n
n
)
2
=
n
(
n
+
1
)
(
2
n
−
1
)
6
n
−
(
n
(
n
+
1
)
2
n
)
2
=
(
n
+
1
)
[
2
n
−
1
6
−
(
n
+
1
)
4
]
=
(
n
+
1
)
12
[
4
n
−
2
−
3
n
−
3
]
=
(
n
+
1
)
12
×
(
n
−
5
)
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