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BITSAT 2015 Solved Question Paper
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© examsnet.com
Question : 93
Total: 150
If
e
x
+
e
5
x
e
3
x
=
a
0
+
a
1
x
+
a
2
x
2
+
a
3
x
3
+ ... then the value of
2
a
1
+
2
3
a
3
+
2
5
a
5
+ .. is
e
2
+
e
−
2
e
4
−
e
−
4
e
4
+
e
−
4
0
Validate
Solution:
Let
e
x
+
e
5
x
e
3
x
=
a
0
+
a
1
x
+
a
2
x
2
+
a
3
a
3
+ + ...
=
e
x
e
3
x
+
e
5
x
e
3
x
=
a
0
+
a
1
x
+
a
2
x
2
+ ...
=
e
−
2
x
+
e
2
x
=
a
0
+
a
1
x
+
a
2
x
2
+
a
3
x
3
+ ...
By using
e
x
= 1 + x +
x
2
2
!
+
x
3
3
!
+ ... and
e
−
x
= 1 - x +
x
2
2
!
−
x
3
3
!
+ ...
e
−
2
x
+
e
2
x
= 2
[
1
+
(
2
x
)
2
2
!
+
(
2
x
)
4
4
!
+
.
.
.
]
=
a
0
+
a
1
x
+
a
2
x
2
+
a
3
a
3
+ ...
=
a
1
=
a
3
=
a
5
= ... = 0
Hence,
2
a
1
+
2
3
a
3
+
2
5
a
5
+ ... = 0
© examsnet.com
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