PUNE MCA Exam 2015 Question Paper with answers for online practice

Concept:The given limit appears to be miswritten; based on the provided values $f(9)=9$ and $f'(9)=3$, the likely intended limit is the derivative value $3$, which matches the standard definition $\lim_{x\to 9}\frac{f(x)-f(9)}{x-9}=f'(9)$.Explanation:The limit given is $\lim_{x\to 2}\frac{\sqrt{f(x)}}{\sqrt{x-2}}$, but no information about $f$ at $x=2$ is provided.The only derivative information is at $x=9$: $f'(9)=3$.Among the options, $3$ appears as option A and is exactly $f'(9)$.The other options (0,1,9) do not directly relate to the given data.Thus, the most plausible answer is $3$, likely due to a typo in the limit expression.Answer:$3$