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AIEEE 2011 Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 67
Total: 91
The coefficient of
x
7
in the expansion of
(
1
−
x
−
x
2
+
x
3
)
6
is
[AIEEE 2011]
−
132
−
144
132
144
Validate
Solution:
Given,
‌
(
1
−
x
−
x
2
+
x
3
)
6
‌
=
[
(
1
−
x
)
−
x
2
(
1
−
x
)
]
6
‌
=
(
1
−
x
)
6
(
1
−
x
2
)
6
=
(
1
+
‌
6
C
1
(
−
x
)
+
‌
6
C
2
(
−
x
)
2
+
‌
6
C
3
(
−
x
)
3
+
.
.
.
.
.
.
)
×
‌
‌
(
1
+
‌
6
C
1
(
−
x
2
)
+
‌
6
C
2
(
−
x
2
)
2
+
‌
6
C
3
(
−
x
2
)
3
+
.
.
.
.
.
.
)
∴
Coefficient of
x
7
=
−
‌
6
C
1
×
−
‌
6
C
3
+
(
−
‌
6
C
3
)
×
‌
6
C
2
+
(
−
‌
6
C
5
)
×
−
‌
6
C
1
=
120
−
300
+
36
=
−
144
© examsnet.com
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