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Byju's Answer
Standard XIII
Mathematics
Sum of Product of Binomial Coefficients
Term independ...
Question
Term independent of
x
in the expansion of
(
x
−
1
x
2
)
3
n
(where
n
is even natural number)
A
3
n
!
n
!
×
2
n
!
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B
3
n
!
n
!
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C
3
n
!
2
n
!
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D
3
n
!
(
n
!
)
2
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Solution
The correct option is
A
3
n
!
n
!
×
2
n
!
T
r
+
1
=
(
−
1
)
r
⋅
3
n
C
r
x
3
n
−
r
×
(
1
x
2
)
r
⇒
T
r
+
1
=
(
−
1
)
r
⋅
3
n
C
r
x
3
n
−
3
r
For independent term
Put
3
n
−
3
r
=
0
⇒
r
=
n
.
So,
T
n
+
1
is free from
x
.
And,
T
n
+
1
=
(
−
1
)
n
⋅
3
n
C
n
=
3
n
C
n
Suggest Corrections
0
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Sum of Product of Binomial Coefficients
Standard XIII Mathematics
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