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Q)

If $^{a^2-a}C_2=^{a^2-a}C_4,$ then $a=?$

$\begin{array}{1 1} 2 \\ 3 \\ 4 \\ 5 \end{array}$

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Toolbox:
  • If $^nC_r=^nC_m$, then either $r=m$ or $r=n-m$
Given: $^{a^2-a}C_2=^{a^2-a}C_4$
$\Rightarrow\:2=a^2-a-4$
$\Rightarrow\:a^2-a-6=0$
$\Rightarrow\:a=3\:\:or\:\:-2$
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