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Question

The sum of the series 20C0−20C1+20C2−20C3+......−......+20C10is−

A
1220C10
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B
0
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C
20C10
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D
20C10
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Solution

The correct option is A 1220C10
We know that,
(1+x)20=20C0+20C1x+20C2x2+20C3x3+............+20C10x10+.............+20C20x20

Putting x=1 we get

0=20C020C1+20C220C3+............+20C10+.............+20C20

But as we know , that 20C0=20C20,20C1=20C19 and so on , we can write above equation as
0=2(20C020C1+20C220C3+..........20C9)+20C1020C102=(20C020C1+20C220C3+..........20C9)

Hence,

20C020C1+20C220C3+............+20C10=20C102+20C10=20C102

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