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Q.

If ∑r=0n r+2r+1nCr=28−16, then n is             (where cr=ncr)

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a

8

b

4

c

6

d

5

answer is D.

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Detailed Solution

∑r=0n r+1r+1+1r+1nCr =∑r=0n nCr+∑r=0n  nCrr+1 =2n+1n+1⋅∑r=0n+1n+1cr+1=2n+2n+1−1n+1=(n+3)2n−1n+1=28−16⇒ n=5
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