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Byju's Answer
Standard XII
Mathematics
Factorial
P n = 1+ x n-...
Question
P
(
n
)
=
(
1
+
x
)
n
−
n
x
−
1
, is divisible by
A
x
3
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B
x
2
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C
any exponent of
x
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D
none of these
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Solution
The correct option is
A
x
2
P
(
n
)
=
(
1
+
x
)
n
−
n
x
−
1
⇒
P
(
n
)
=
1
+
n
x
+
n
C
2
x
2
+
.
.
.
+
n
C
n
x
n
−
1
−
n
x
=
x
2
(
n
C
2
+
n
C
3
x
+
.
.
.
+
n
C
n
x
n
−
2
)
Therefore,
P
(
n
)
is divisible by
x
2
Ans: B
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