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KVPY SB SX Exam 2011 Question Paper
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© examsnet.com
Question : 2
Total: 120
Suppose n is a natural number such that
|
i
+
2
i
2
+
3
i
3
+
.
.
.
+
n
i
n
=
18
√
2
|
. where i is the square root of -1. Then n is
9
18
36
72
Validate
Solution:
S
=
i
+
2
i
2
+
3
i
3
+
.
.
.
.
.
+
n
i
n
i
S
=
i
2
+
2
i
3
+
.
.
.
.
.
+
(
n
−
1
)
i
n
+
n
i
n
+
1
S
(
1
−
i
)
=
i
+
i
2
+
i
3
+
.
.
.
.
.
+
i
n
−
n
i
n
+
1
S
(
1
−
i
)
=
i
(
1
−
i
n
)
1
−
i
−
n
i
n
+
1
⇒
S
=
1
−
i
n
−
2
i
↓
z
1
(
s
a
y
)
−
n
i
n
+
i
1
−
i
↓
z
2
(
s
a
y
)
|
z
1
|
=
1
√
2
or
0
|
z
2
|
=
n
√
2
=
n
2
√
2
n
2
=
18
⇒
n
=
36
© examsnet.com
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