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Q.

3003010−3013011+…+30203030 is equal to

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a

30C11

b

60C10

c

30C10

d

65C55

answer is C.

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Detailed Solution

Let A=3003010−3013011+3023012−…+30203030 or A=30C0⋅30C10−30C1⋅30C11+30C2⋅30C12−…+30C20⋅30C30 = Coefficient of x20 in (1+x)30(1−x)30= Coefficient of x20 in 1−x230= Coefficient of x20 in ∑r=030 (−1)r30Crx2r=(−1)10 30C10 [for coefficient of x20, let r=10=30C10=(−1)10 30C10 [for coefficient of x20, let r=10=30C10

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