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BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM2 Marks
Question
Find the coefficients of : $a^5 b^7$ in $(a - 2b)^{12}$
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Answer

Here general term of the expansion $(a - 2b)^{12}$ is
$T_{r+1}=^{12}C_ra^{12-r}{(-2b)^r}$. . . (i)
Now $12 - r = 5$ and $r = 7$
$ \Rightarrow r = 12 - 5 = 7$
Putting $r = 7$ in (i)
$\therefore {T_8}{ = ^{12}}{C_7}{(a)^5}{( - 2b)^7}$${ = ^{12}}{C_7}{( - 2)^7}{a^5}{b^7}$
$\therefore $ Coefficient of $a^5 b^7$ in the expansion ${(a - 2b)^{12}}{ = ^{12}}{C_7}{( - 2)^7}$
$ = 792 \times - 128 = - 101376$

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