Consider an equation \( \log _{2}\left(\alpha^{6}-16 \alpha^{3}+66\...

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Consider an equation \( \log _{2}\left(\alpha^{6}-16 \alpha^{3}+66\right)+\sqrt{4 \beta^{4}-8 \beta^{2}+13}+\left|\left[\frac{\gamma}{3}-2\right]\right|=4 \),
P where \( \alpha, \beta, \gamma \) are integers and \( m, n \) and \( r \) are the number of values of \( \alpha, \beta \) and

W \( \gamma \) respectively which satisfy the above equation.
[Note \( :[y] \) denotes greatest integer function of \( y \).]
The value of \( \lim _{x \rightarrow 0} \sum_{i=1}^{r}\left[\frac{\sin \left(\gamma_{i} x\right)}{x}\right] \) is equal to (where \( \gamma_{1}, \gamma_{2}, \ldots \ldots \gamma_{\mathrm{r}} \) are the values of \( \gamma \) )
(a) 17
(b) 18
(c) 19
(d) 21
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