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If for positive integers $r > 1, n > 2$ , the coefficient of the (3r)th and (r + 2)th powers of X in the expansion of (1 + x)²ⁿ are equal, then

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n=2r

n=3r

n=2r+1

None of these

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detailed solution

Correct option is C

In the expansion of (1+x)2n , the general termAs given for=2nCkxk,0≤k≤2n r>1,n>2,2nC3r=2nCr+2⇒ Either 3r=r+2 or 3r=2n−(r+2)∵nCr=nCn−rr=1 or n=2r+1We take the relation onIyn=2r+1 [∵r>1]

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If for positive integers r>1,n>2, the coefficient of the (3r)th and (r + 2)th powers of X in the expansion of (1 + x)2n are equal, then

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If for positive integers $r > 1, n > 2$ , the coefficient of the (3r)th and (r + 2)th powers of X in the expansion of (1 + x)²ⁿ are equal, then