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Byju's Answer
Standard XII
Mathematics
Binomial Coefficients
Find the term...
Question
Find the term which has the exponent of x as 8 in the expansion of
⎛
⎜
⎝
x
5
2
−
3
x
3
√
x
⎞
⎟
⎠
10
A
T
2
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B
T
3
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C
T
4
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D
Does not exist
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Solution
The correct option is
C
Does not exist
Given,
⎛
⎜
⎝
x
5
2
−
3
x
3
√
x
⎞
⎟
⎠
10
General term,
T
r
+
1
=
n
C
r
x
n
−
r
y
r
T
r
+
1
=
10
C
r
(
x
5
2
)
10
−
r
(
−
3
x
3
√
x
)
r
T
r
+
1
=
10
C
r
(
x
)
25
−
5
r
2
(
−
3
)
r
x
7
2
r
T
r
+
1
=
10
C
r
(
−
3
)
r
(
x
)
25
−
6
r
given the exponent of x as
8
25
−
6
r
=
8
25
−
8
=
6
r
6
r
=
17
r
=
17
6
since r is a fraction number which is not possible. Hence, the term which has the exponents of x as
8
in the expansion of
⎛
⎜
⎝
x
5
2
−
3
x
3
√
x
⎞
⎟
⎠
10
does not exist.
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1
Similar questions
Q.
lf
t
0
,
t
1
,
t
2
,
t
n
are the consecutive terms in the expansion
(
x
+
a
i
)
n
, then
(
t
0
−
t
2
+
t
4
−
t
6
+
…
.
)
2
+
(
t
1
−
t
3
+
t
5
…
.
)
2
=
Q.
If
T
0
,
T
1
,
T
2
,
.
.
.
.
.
T
n
represent the term in the expansion of
(
x
+
a
)
n
, then the value of
(
T
0
−
T
2
+
T
4
−
T
6
+
.
.
.
.
.
)
2
+
(
T
1
−
T
3
+
T
5
+
.
.
.
.
.
)
2
is
Q.
If
T
0
,
T
1
,
T
2
,
.
.
.
,
T
n
represent in the terms in the expansion of
(
x
+
a
)
n
, then the value of
(
T
0
−
T
2
+
T
4
−
T
6
+
.
.
.
)
2
+
(
T
1
−
T
3
+
T
5
+
.
.
.
)
2
is equal to
Q.
If
T
0
,
T
1
,
⋯
,
T
n
represent the terms in the expansion of
(
x
+
a
)
n
, then the value of
(
T
0
−
T
2
+
T
4
−
⋯
)
2
+
(
T
1
−
T
3
+
T
5
−
⋯
)
2
is
Q.
If
t
2
t
3
in the expansion of
(
a
+
b
)
n
and
t
3
t
4
in the expansion of
(
a
+
b
)
n
+
3
are equal, then find the value of
n
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