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Question

Given positive integers r>1,n>2 and the coefficient of (3r)th and (r+2)th terms in the binomial expansion of (1+x)2n are equal, then

A
n=2r
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B
n=2r+1
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C
n=3r
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D
None of these
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Solution

The correct option is A n=2r
3r th term in the expansion of (1+x)2n

=2nC3r1x3r1

and (r+2)th term in the expansion of (1+x)

=2nCr+1xr+1

Given that the binomial coefficients of (3r1) and (r+2)th terms are equal.

Thus 2nC3r1=2nCr+1

3r1=r+1

or 2n=(3r1)+(r+1)

2r=2 or 2n=4r

r=1 or n=2r

But r>1

Therefore, n=2r

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