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Question

The sum of the series 20C0 - 20C1 + 20C2 - 20C3 ...............+ 20C10 is


A

20C10

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B

1220C10

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C

0

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D

20C10

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Solution

The correct option is B

1220C10


Consider the expansion of (1+x)20

(1+x)20 = 20C0+20C1x+20C2x2..........20C10x10+20C11x11+20C12x12..........20C20x20

Put x = -1

20C0 - 20C1 + 20C2 .............+20C9+20C1020C11+20C12 + ............ + 20C20

= (20C020C1+20C2...........20C9)+20C10+(20C11+20C12+..............+20C20)

20C0=20C20,20C1=20C19,.........20C9=20C11

20=2×(20C020C1+........20C9)+20C10

+ 20C10=2(20C020C1+20C2........20C9)+2×20C10

(Adding 20C10 on both the sides)

20C102 = (20C020C1+20C2.........20C10)


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