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Question
Mathematics
The value of (21C1 - 10C1) + (21C2 - 10C2) + (21C3 - 10C3) +(21C4 - 10C4) +....+(21C10 - 10C10) is :
Q. The value of
(
21
C
1
−
10
C
1
)
+
(
21
C
2
−
10
C
2
)
+
(
21
C
3
−
10
C
3
)
+
(
21
C
4
−
10
C
4
)
+
....
+
(
21
C
10
−
10
C
10
)
is :
3940
210
JEE Main
JEE Main 2017
Binomial Theorem
Report Error
A
2
21
−
2
10
42%
B
2
20
−
2
9
18%
C
2
20
−
2
10
14%
D
2
21
−
2
11
26%
Solution:
=
21
C
1
+
21
C
2
+
...
+
21
C
10
2
1
{
21
C
0
+
21
C
1
+
...
+
21
C
21
}
−
1
=
2
20
−
1
(
10
C
1
+
10
C
2
+
...
+
10
C
10
)
=
2
10
−
1
∴
Required sum
=
(
2
20
−
1
)
−
(
2
10
−
1
)
=
2
20
−
2
10