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Questions  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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Q)

The ratio of the coefficients of $x^p$ and $x^q$ in the expansion of $(1+x)^{p+q}$ is

$\begin{array}{1 1}(A)\;1\\(B)\;2\\(C)\;3\\(D)\;4\end{array} $

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A)
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  • $T_{r+1}=nC_r a^{n-r} b^r$
$T_{r+1}=(p+q) C_r a^{p+q-r} b^r$
Coefficient of $x^p$ and $x^q$ in the expansion of $(1+x)^{p+q}$ are $p+qC_p$ and $p+qC_q$
$\Rightarrow p+qC_p=p+q C_q$
$\Rightarrow \large\frac{(p+q)!}{(p+q)!}$
$\Rightarrow 1$
Hence (A) is the correct answer.
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