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UPSC NDA 2 2019 Mathematics Solved Paper
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© examsnet.com
Question : 25
Total: 120
If the middle term in the expansion of
(
x
2
+
1
x
)
2
n
is
184756
x
10
, then what is the value of n?
[NDA II 2019]
10
8
5
4
Validate
Solution:
👈: Video Solution
The given expression
=
(
x
2
+
1
x
)
2
n
Here, n = 2n, which is an even number.
So,
(
2
n
2
+
1
)
t
h
i.e.,
(
n
+
1
)
th term is the middle term
Now,
T
n
+
1
=
2
n
C
n
(
x
2
)
2
n
−
n
⋅
(
1
x
)
n
=
2
n
C
n
⋅
(
x
2
)
n
×
x
−
n
=
2
n
C
n
⋅
x
2
n
⋅
x
−
n
=
2
n
C
n
⋅
x
2
n
−
n
=
2
n
C
n
⋅
x
n
Given, Middle term
=
184756
x
10
2
n
C
n
x
n
=
184756
x
10
⇒
2n
n
2n-n
x
n
=
184756
x
10
⇒
2n
n
n
x
n
=
184756
x
10
⇒
20
10
10
x
n
=
184756
x
10
Hence,
n
=
10
© examsnet.com
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