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Standard XII
Maths
Question
If the coefficient of
x
3
and
x
4
in the expansion of
(
1
+
a
x
+
b
x
2
)
(
1
−
2
x
)
18
in powers of
x
are both zero, then
(
a
,
b
)
is equal to
(
16
,
251
3
)
(
14
,
251
3
)
(
14
,
272
3
)
(
16
,
272
3
)
A
(
16
,
251
3
)
B
(
14
,
251
3
)
C
(
14
,
272
3
)
D
(
16
,
272
3
)
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Solution
Verified by Toppr
Given expression is
(
1
+
a
x
+
b
x
2
)
(
1
−
2
x
)
18
=
(
1
+
a
x
+
b
x
2
)
(
1
−
18
C
1
(
2
x
)
+
18
C
2
(
2
x
)
2
−
18
C
3
(
2
x
)
3
+
.
.
.
.
18
C
18
(
2
x
)
18
)
Now, coefficient of
x
3
=
−
18
C
1
(
2
b
)
+
a
×
18
C
2
(
4
)
−
18
C
3
(
8
)
=
0
∴
34
a
=
b
+
34
×
16
3
.
.
.
(
i
)
Similarly, a coefficient of
x
4
18
C
4
(
4
)
−
18
C
3
(
2
a
)
+
18
C
2
(
b
)
=
0
.
.
.
(
i
i
)
From
(
i
)
and
(
i
i
)
,
a
=
16
and
b
=
272
3
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in the powers of
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