JEE Math Practice Question
Consider the function. $$ f(x)=\left\{\begin{array}{cc} \frac{\mathrm{a}\left(7 x-12-x^2\right)}{\mathrm{b}\left|x^2-7 x+12\right|} & , x3 \\\\ \mathrm{~b} & , x=3, \end{array}\right. $$ where $[x]$ denotes the greatest integer less than or equal to $x$. If $\mathrm{S}$ denotes the set of all ordered pairs (a, b) such that $f(x)$ is continuous at $x=3$, then the number of elements in $\mathrm{S}$ is :
- A.Infinitely many
- B.4
- C.2
- D.1
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