List of top Mathematics Questions on Limit and Continuity asked in KEAM

The value of $\lim_{x\rightarrow 2^{+}}\frac{[x]-2}{x-2}$ is

Let $f(x)=\begin{cases}ax+3 & x<1\\ \frac{4x}{a} & x\ge 1\end{cases}$. If $\lim_{x\rightarrow 1}f(x)$ exists, then the possible values of $a$ are