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Question

If nC4, nC5, nC6 of (1+x)n are in A.P. then n=

A
12
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B
11
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C
7
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D
8
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Solution

The correct option is C 7
Let nCr1,nCr,nCr+1 be in AP.
Therefore condition for the following terms to be in A.P is
(n2r)2=n+2 ...(i)
In the above question
nCr1=nC4
Hence r1=4
r=5
Substituting in (i), we get
(n10)2=n+2
n220n+100=n+2
n221n+98=0
(n14)(n7)=0
n=7 and n=14
Hence, answer is option C

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