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Standard XII
Maths
Question
If the fourth term in the expansion of
(
p
x
+
1
/
x
)
n
is
5
/
2
then the value of p is?
1
1
/
2
6
2
A
1
/
2
B
1
C
6
D
2
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Solution
Verified by Toppr
(
p
x
+
1
x
)
n
=
n
C
0
(
1
x
)
0
(
p
x
)
n
−
0
+
n
C
1
(
1
x
)
1
(
p
x
)
n
−
1
+
.
.
.
+
n
C
n
(
1
x
)
n
(
p
x
)
n
−
1
so, the fourth in the expansion is,
n
C
3
(
1
x
)
3
(
p
x
)
n
−
3
But given the fourth term is
5
2
which is independent
of x. So,
n
−
3
−
3
=
0
⇒
n
=
6
Now,
6
C
3
.
P
3
=
5
2
⇒
20
P
3
=
5
2
⇒
p
3
=
1
8
⇒
p
=
1
2
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