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Solution
It is given,
$$5^a=9^b=2025$$
$$5^a=2025$$
Applying log on both the sides, we get
$$\log_55^a=\log_52025$$
$$a=\log_52025$$
Similarly, we get $$b=\log_92025$$
$$\dfrac{ab}{a+b}=\dfrac{1}{\dfrac{1}{a}+\dfrac{1}{b}}$$
$$\dfrac{1}{a}=\log_{2025}5$$
$$\dfrac{1}{b}=\log_{2025}9$$
$$\dfrac{1}{a}+\dfrac{1}{b}=\log_{2025}45$$
$$\dfrac{ab}{a+b}=\log_{45}2025\ =\ 2$$
The answer is option C.
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