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Byju's Answer
Standard XII
Mathematics
Binomial Theorem for Any Index
In the expans...
Question
In the expansion of
a
+
b
x
e
x
, the coefficient of
x
r
is
A
a
−
b
r
!
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B
a
−
b
r
r
!
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C
(
−
1
)
r
a
−
b
r
r
!
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D
None of these
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Solution
The correct option is
C
(
−
1
)
r
a
−
b
r
r
!
(
a
+
b
x
)
e
−
x
=
(
a
+
b
x
)
{
1
−
x
1
!
+
x
2
2
!
−
x
3
3
!
+
.
.
.
+
(
−
1
)
n
x
n
n
!
+
.
.
.
.
}
∴
The coefficient of
x
r
=
a
(
−
1
)
r
r
!
+
b
(
−
1
)
r
−
1
(
r
−
1
)
!
=
a
(
−
1
)
r
r
!
−
b
r
(
−
1
)
r
(
r
)
!
=
(
−
1
)
r
r
!
(
a
−
b
r
)
Suggest Corrections
0
Similar questions
Q.
For
r
=
0
,
1
,
2
,
,
.
.
.
.10
let
A
r
,
B
r
and
C
r
denote respectively the coefficient of
x
r
in the expansions of
(
1
+
x
)
10
,
(
1
+
x
)
20
and
(
1
+
x
)
30
. Then
∑
10
r
=
1
A
r
(
B
10
B
r
−
C
10
A
r
)
is equal to
Q.
For
r
=
0
,
1
,
.
.
.
.
,
10
, let
A
r
,
B
r
and
C
r
denote, respectively, the coefficient of
x
r
in the expansions of
(
1
+
x
)
10
,
(
1
+
x
)
20
and
(
1
+
x
)
30
. Then,
∑
10
r
=
1
A
r
(
B
10
B
r
−
C
10
A
r
)
is equal to -
Q.
For r=0,1,2,........10, let
A
r
,
B
r
and
C
r
denote respectively the coefficient of
x
r
in the expansions of
(
1
+
x
)
10
,
(
1
+
x
)
20
and
(
1
+
x
)
30
. Then
10
∑
r
=
1
A
r
(
B
10
B
r
−
C
10
A
r
)
is
Q.
In the expansion of
3
−
x
(
1
−
x
)
2
coefficient of
x
r
is
10
then
r
=
Q.
For
r
=
0
,
1
,
2
,
3
,
.
.
.
,
10
, let
A
r
,
B
r
,
C
r
denote respectively the coefficient of
x
r
in the expansions of
(
1
+
x
)
10
,
(
1
+
x
)
20
and
(
1
+
x
)
30
. Then
∑
10
r
=
1
A
r
(
B
10
B
r
−
C
10
A
r
)
is equal to
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