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NIMCET 2023 Question Paper with solutions
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© examsnet.com
Question : 5
Total: 120
Which of the following number is the coefficient of
x
100
in the expansion of
log
e
(
1
+
x
1
+
x
2
)
,
|
x
|
<
1
?
−
0.03
−
0.01
0.01
0.02
Validate
Solution:
log
e
(
1
+
x
)
=
x
−
x
2
2
+
x
3
3
−
x
4
4
+
x
5
5
−
.
.
.
−
x
100
100
+
.
.
.
ln
(
1
+
x
)
2
=
x
2
−
x
4
2
+
x
6
3
−
x
8
4
+
.
.
.
−
(
x
2
)
50
50
∴
Coefficient of
x
100
in
ln
(
1
+
x
1
+
x
2
)
Coefficient of
x
100
in
ln
(
1
+
x
)
−
ln
(
1
+
x
2
)
=
−
1
100
+
1
50
=
0.01
.
© examsnet.com
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