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Question

The coefficient of x9 in the polynomial given by 11t=1(x+r)(x+r+1)(x+r+2)........(x+r+9) is

A
5511
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B
5151
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C
1515
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D
1155
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Solution

The correct option is C 1155
Coeff.ofx9qn11r=1(x+r)(x+r+1)(x+r+2).....(x+r+9)=11r=1Coff.ofx9in(x+r)(x+r+1)(x+r+2)+....(x+r+9)=11r=1r+(r+1)+(r+2)+(r+3)+.....+(r+9)=11r=1[10r+(1+2+3...9)]=1011r=1r+4511r=1.1=10×11×122+45×11=660+495=1155Hence,theoptionDisthecorrectanswer.

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