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Question

If f(x)=1+x2−x3+...−x15+x16−x17, then the coefficient of x2 in f(x−1) is

A
826
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B
816
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C
822
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D
none of these
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Solution

The correct option is B 816
The coefficient of x2 will be
2C2+3C2+4C2+5C2+...17C2
Applying nCr+nCr+1=n+1Cr+1
The above expression simplifies to
[1+3C3+3C2+4C2+5C2+...17C2]3C3
=[1+17C3+17C2]1
=1+18C31
=18C3
=816

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