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Byju's Answer
Standard XIII
Mathematics
General Term of Binomial Expansion
In the expans...
Question
In the expansion of
(
x
3
−
1
x
2
)
n
,
n
∈
N
, if the sum of the coefficients of
x
5
and
x
10
is
0
, then
n
is
A
25
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B
20
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C
15
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D
10
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Solution
The correct option is
C
15
(
x
3
−
1
x
2
)
n
General term
T
r
+
1
=
n
!
r
!
(
n
−
r
)
!
(
−
1
)
n
−
r
x
5
r
−
2
n
If
5
r
−
2
n
=
5
, then
5
r
=
2
n
+
5
or
r
=
2
n
5
+
1
If
5
r
−
2
n
=
10
, then
5
r
=
2
n
+
10
or
r
=
2
n
5
+
2
x
5
and
x
10
terms occur if
n
=
5
k
Given, the sum of coefficients
x
5
and
x
10
is zero.
⇒
(
5
k
)
!
(
2
k
+
1
)
!
(
3
k
−
1
)
!
−
(
5
k
)
!
(
2
k
+
2
)
!
(
3
k
−
2
)
!
=
0
or,
1
3
k
−
1
−
1
2
k
+
2
=
0
or,
k
=
3
⇒
n
=
15
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0
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