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Question
Mathematics
The coefficient of x7 in the expansion of (1- x - x2 + x3 )6 is
Q. The coefficient of
x
7
in the expansion of
(
1
−
x
−
x
2
+
x
3
)
6
is
6478
208
AIEEE
AIEEE 2011
Binomial Theorem
Report Error
A
- 132
7%
B
- 144
43%
C
132
29%
D
144
21%
Solution:
(
1
−
x
−
x
2
+
x
3
)
6
=
[(
1
−
x
)
−
x
2
(
1
−
x
)
]
6
=
(
1
−
x
)
6
(
1
−
x
2
)
6
=
(
1
−
6
x
+
15
x
2
−
20
x
3
+
15
x
4
−
6
x
5
+
x
6
)
×
(
1
−
6
x
2
+
15
x
4
−
20
x
6
+
15
x
8
−
6
x
10
+
x
12
)
Coefficient of
x
7
=
(
−
6
)
(
−
20
)
+
(
−
20
)
(
15
)
+
(
−
6
)
(
−
6
)
=
−
144