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NDA Math Binomial Theorem
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© examsnet.com
Question : 12
Total: 50
What is the coefficient of the middle term in the expansion of
(
1
+
4
x
+
4
x
2
)
5
?
[NDA-I 2021]
8064
4032
2016
1008
Validate
Solution:
👈: Video Solution
Concept
(
1
−
x
)
n
=
n
∑
k
=
0
(
n
r
)
1
n
−
k
(
−
x
)
k
Given:
1
+
4
x
+
4
x
2
)
5
=
[
(
1
+
2
x
)
2
]
5
=
(
1
+
2
x
)
10
For Middile term:
r
=
10
∕
2
=
5
Middile Term
=
10
C
5
(
1
)
5
(
2
x
)
5
=
10
!
5
!
5
!
32
x
5
=
8064
x
5
The coefficient of the middle term in the expansion of
(
1
+
4
x
+
4
x
2
)
5
is 8064
© examsnet.com
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