Consider the function. $f(x) = \begin{cases} \frac{a(7x-12-x^2)}{bx^2-7x+12}, & x3 \ b, & x=3 \end{cases}$ Where $[x]$ denotes the greatest integer less than or equal to $x$. If $S$ denotes the set of all ordered pairs $(a, b)$ such that $f(x)$ is continuous at $x = 3$, then the number of elements in $S$ is :

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Consider the function. $f(x) = \begin{cases} \frac{a(7x-12-x^2)}{bx^2-7x+12}, & x<3 \ \frac{\sin(x-3)}{2^{x-[x]}}, & x>3 \ b, & x=3 \end{cases}$ Where $[x]$ denotes the greatest integer less than or equal to $x$. If $S$ denotes the set of all ordered pairs $(a, b)$ such that $f(x)$ is continuous at $x = 3$, then the number of elements in $S$ is :

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