Q.
Consider an equation $\log _2\left(\alpha^6-16 \alpha^3+66\right)+\sqrt{4 \beta^4-8 \beta^2+13}+\left|\left[\frac{\gamma}{3}-2\right]\right|=4$ and $m , n$ and $r$ are the number of integral values of $\alpha, \beta$ and $\gamma$ respectively which satisfy the above equation.
The value of $\displaystyle\lim _{x \rightarrow 0} \sum_{i=1}^r\left[\frac{\sin \left(\gamma_i \cdot x\right)}{x}\right]$ is equal to (where $\gamma_1, \gamma_2, \ldots . . \gamma_t$ are the values of $\gamma$ )
Conic Sections
Solution: