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# Let $S_p$ and $S_q$ be the coefficient of $x6p$ and $x^q$ respectively in $(1+x)^{p+q}$ then

$\begin{array}{1 1}(A)\;S_p\neq S_q\\(B)\;S_p=\large\frac{q}{p}\normalsize S_q\\(C)\;S_p=\large\frac{p}{q}\normalsize S_q\\(D)\;S_p=S_q\end{array}$

Can you answer this question?

$S_p$-Coefficient of $x^p=p+qC_p=\large\frac{(p+q)!}{p!q!}$
$S_q$-Coefficient of $x^q=p+qC_q=\large\frac{(p+q)!}{p!q!}$
$\therefore S_p=S_q$
Hence (D) is the correct answer.
answered Jun 26, 2014