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Question

Find the coefficient of a5b7 in (a−2b)12

A
12356
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B
-101356
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C
101376
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D
-101376
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Solution

The correct option is D -101376
It is know that (r+1)th term (Tr+1) in the binomial expansion
of (a+b)n is given by Tr+1=nCraarbr
Assuming that a5b7 occurs in the
(r+1)th term of the expansion (a2b)12 we obtain
Tr+1=12Cr(a)12r(2b)r=12Cr(2)r(a)12r(b)r
Comparing the indices of a and b in a5b7 and in Tr+1, we obtain r=7
Thus the coefficient of a5b7 is
=12C7(2)7=12!7!5!×27=12.11.10.9.8.7!5.4.3.2.7!.27=(792)(128)=101376

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