Q.

The coefficient of   x7 in the expansion of 1−x−x2+x36is

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answer is 4.

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Detailed Solution

1−x−x2+x36=(1−x)61−x26coefficient of x7 in  1−6C1x+6C2x2−⋯+6C6x6= coefficient of in 1−6C1x+6C2x2−⋯+6C6x6×1−6C1x2+6C2x4−⋯+6C6x12              =−6C1−6C3+−6C3 6C2+−6C5−6C1=−144
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