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Question

Coefficient of a5b7 in (a−2b) 12 is

A
101376
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B
201356
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C
31064
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D
None
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Solution

The correct option is A 101376
(a2b)12=[a+(2b)]12
General term Tr+1=C(12,r)a12r(2b)r
Putting 12r=5 or 125=rr=7
T7+1=C(12,7)a127(2b)7=C(12,7)a5(2b)7=C(12,7)(2)7a5b7
Hence required coefficient is C(12,7)(2)7=!2!7!5!27=12×11×10×9×8×7!7!×5×4×3×2×1×27
=11×9×27=99×128=101376

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