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Question

If 12x+1{(1+2x+1)n(12x+1)n}=a0+a1x+a2x2+....+anxn then n must be equal to

A
20,21
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B
21,22
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C
22,23
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D
none of these
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Solution

The correct option is A 21,22
12x+1{(1+2x+1)n(12x+1)n}
=2{nC1+nC3(2x+1)+nC5(2x+1)2+....}
For R.H.S to be polynomial of degree 10, the last term of R.H.S must
nC21(2x+1)10
This can happen if n=21 or 22

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