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Byju's Answer
Standard XII
Mathematics
Permutations and Combinations
If number of ...
Question
If number of terms in the expansion of
(
1
+
4
x
+
x
2
)
n
,
n
∈
N
is
1225
, then the value of
n
is-
A
48
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B
408
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C
612
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D
1244
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Solution
The correct option is
B
48
We know that number of terms in expansion of
(
x
1
+
x
2
+
x
3
+
.
.
.
.
.
+
x
r
)
n
is
n
+
r
−
1
C
n
.
Hence number of terms in
(
1
+
4
x
+
x
2
)
n
is
n
+
3
−
1
C
n
=
n
+
2
C
2
=
1225
(given)
⇒
(
n
+
2
)
(
n
+
1
)
2
=
1225
⇒
(
n
+
2
)
(
n
+
1
)
=
2450
⇒
n
2
+
3
n
−
2448
=
0
⇒
n
=
48
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0
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