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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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Find the $4^{th}$ term in the expansion of $(x-2y)^{12}$

$\begin{array}{1 1}(A)\;-1760\\(B)\;-760x^9\\(C)\;-1760x^9y^3\\(D)\;x^9y^3\end{array} $

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1 Answer

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Toolbox:
  • $(a-b)^n=nC_0a^n-nC_1a^{n-1}b+nC_2a^{n-2}b^2-......+(-1)^nnC_ra^{n-r}b^r+......nC_n(-b)^n$
$4^{th}$ term =$T_{3+1}$ in the expansion of $x+(-2y)^{12}$
$\Rightarrow 12C_3x^{12-3}[-2y]^3$
$\Rightarrow \large\frac{12.11.10}{1.2.3}$$x^9(-1)^3.2^3.y^3$
$\Rightarrow -220\times 8.x^9.y^3$
$\Rightarrow -1760x^9y^3$
Hence (C) is the correct answer.
answered Jun 23, 2014 by sreemathi.v
 
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