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AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper
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© examsnet.com
Question : 19
Total: 160
The numerically greatest term in the binomial expansion of
(
2
a
−
3
b
)
19
when
a
=
1
4
and
b
=
2
3
is
19
C
5
.2
11
19
C
3.1
2
11
19
C
4.1
2
13
19
C
3.2
13
Validate
Solution:
On expanding the given expression.
(
2
a
−
3
b
)
19
=
2
19
.
a
19
(
1
−
3
b
2
a
)
19
The r
th
term of greatest term is,
(
1
+
x
)
n
=
[
(
n
+
1
)
|
x
|
1
+
|
x
|
]
Here,
n
=
19
,
x
=
−
3
b
2
a
∴
r
=
[
20
|
3
b
2
a
|
1
+
3
b
2
a
]
=
[
20
1
+
4
×
4
]
r
=
16
The greatest term of
(
2
a
−
3
b
)
13
is,
(
2
a
−
3
b
)
19
=
19
C
16
×
2
19
.
a
19
[
3
b
2
a
]
16
(
2
a
−
3
b
)
14
=
19
C
16
×
2
19
.
(
1
4
)
19
(
4
)
16
=
19
C
3
×
2
13
© examsnet.com
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