The term independent of x in the binomial expansion of(2/x²-√x)¹⁰ is equal to. ( a.) 180. ( b.)120. ( c.)90. ( d.)72 show the full solution. no spam please
Answers
Answer:
Given expansion of (1−x/1 +3x^5) (2x^2
−
x
1
)
8
For this, we write general term in the expansion of (2x
2
−
x
1
)
8
T
r+1
=
8
C
r
(2x
2
)
8−r
(
x
1
)
−r
=
8
C
r
2
8−r
(x
16−3r
)
Now, in the product (1−
x
1
+3x
5
)(2x
2
+(−
x
1
)
8
, the term independent of x is
1× term not containing x in (2x
2
−
x
1
)
8
−
x
1
× term containing x in (2x
2
−
x
1
)
8
+3x
5
× term containing x
−5
in
(2x
2
−
x
1
)
8
.....(2)
Now, by (1), term without x ,
16−3r=0
⇒r=
3
16
which is not possible.
Hence, there is no term independent of x in (2x
2
−
x
1
)
8
Now, again by (1), term containing x
16−3r=1
⇒r=5
So, by (1), T
6
=−448x
Now, again by (1), term containing x
−5
16−3r=−5
⇒r=7
So, by (1), T
8
=−16x
−5
Put all these values in (2), we get
Term independent of x=1×0 −
x
1
(−448x) +3x
5
(−16x
−5
)
=448−48=400
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Answer:
answer will be option c
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