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Q.

If (1+x)n=nC0+nC1x+nC2x2+.+nCnxn where  nC0, nC1, nC2, are binomial coefficients, then 2C0+C3+C6+.+C1+C4+C7+(1+ω)+C2+C5+C8+..1+ω2, where ω is the cube root of unity and n is a multiple of 3, then the above expression is equal to

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a

2n+1

b

2n+11

c

2n1

d

2n1+1

answer is D.

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Detailed Solution

(1+ω)n=C0+C1ω+C2ω2+.Cnωn(1+1)n=C0+C1+C2+Cn(1+ω)n+2n=2C0+C1(1+ω)+C21+ω2+.=2n+(1)nω2n=2n1, n3λ

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