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If ${ }^n C_r$ denotes the number of combinations of $n$ distinct things taken $r$ at a time, then the domain of the function $g(x)={ }^{(16-x)} C_{(2 x-1)}$ is
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The correct answer is:
$\{1,2,3,4,5\}$
$g(x)={ }^{16-x} \mathrm{C}_{2 x-1}$
$16-x>0$ and $2 x-1 \geq 0$ and $16-x \geq 2 x-1$ $x < 16$ and $x \geq \frac{1}{2}$ and $x \leq \frac{17}{3}$
Also $x$ must be integer
$$
\therefore x \in\{1,2,3,4,5\}
$$
$16-x>0$ and $2 x-1 \geq 0$ and $16-x \geq 2 x-1$ $x < 16$ and $x \geq \frac{1}{2}$ and $x \leq \frac{17}{3}$
Also $x$ must be integer
$$
\therefore x \in\{1,2,3,4,5\}
$$
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