JEE (Advanced) 2019 Paper-2 Question 40

Question 40

Let $$f: R \rightarrow R$$ bea function. We say that f has
PROPERTY 1 if $$\lim_{h \rightarrow 0} \frac{f(h) - f(0)}{\sqrt{|h|}}$$ exists and is finite, and
PROPERTY 2 if $$\lim_{h \rightarrow 0} \frac{f(h) - f(0)}{h^2}$$ exists and is finite.
Then which of the following options is/are correct?



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