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Q.

If  nC0,nC1,nC2,,nCn are binomial coefficients of different terms in the expansion of (1+x)n,(nN) then 1+ nC1 nC01+ nC2 nC11+ nC3 nC21+ nCn nCn1 equals to

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a

n+1nn

b

(n+1)!n!n

c

(n+1)nn!

d

None of these

answer is C.

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Detailed Solution

1+ nC1 nC01+ nC2 nC11+ nC3 nC21+ nCn nCn1

1+n11+n121+n231+1n

(1+n)1(1+n)2(1+n)n nCr nCr1=nr+1r

=(1+n)nn!

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