The value of 11C1 + 2 × 11C2 + 3 × 11C3 + … + 11 × 11C11 is
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Correct option is B)
We know,
(1+x)
11
=
11
C
0
+
11
C
1
x+
11
C
2
x
2
+....+
11
C
11
x
11
Integrating both sides with respect to x:
12
(1+x)
12
=
11
C
0
1
x
+
11
C
1
2
x
2
+
11
C
2
3
x
3
+....+
11
C
11
12
x
12
Putting x=1
12
(2)
12
=
1
11
C
0
+
2
11
C
1
+
3
11
C
2
+....+
12
11
C
11
1
11
C
0
+
2
11
C
1
+
3
11
C
2
+....+
11
11
C
10
=
12
2
12
−
12
1
=
12
2
12
−1
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