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NDA Math Binomial Theorem
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© examsnet.com
Question : 22
Total: 50
How many terms are there in the expansion of
(
1
+
2
x
+
x
2
)
5
+
(
1
+
4
y
+
4
y
2
)
5
?
[NDA II 2019]
12
20
21
22
Validate
Solution:
(
1
+
2
x
+
x
2
)
5
+
(
1
+
4
y
+
4
y
2
)
5
=
[
(
1
+
x
)
2
]
5
+
[
(
1
+
2
y
)
2
]
5
=
(
1
+
x
)
10
+
(
1
+
2
y
)
10
=
(
10
C
0
(
1
)
10
−
0
⋅
x
0
+
10
C
1
⋅
1
⋅
x
1
+
.
.
.
+
10
C
10
⋅
1
⋅
x
10
)
+
(
10
C
0
⋅
1
⋅
y
0
+
10
C
1
⋅
1
⋅
y
1
+
.
.
.
+
10
C
10
⋅
1
⋅
y
10
)
=
1
+
10
C
1
⋅
x
+
.
.
.
+
1
⋅
x
10
+
1
+
10
C
1
⋅
y
+
.
.
.
+
y
10
=
(
2
+
10
C
1
x
+
.
.
.
+
x
10
)
+
(
10
C
1
y
+
.
.
.
+
y
10
)
Here, the number of terms
=
11
+
10
=
21
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