**Solution**:

Let the mean proportion be $x$.

Then, $4: x:: x: 25$

$$

\begin{array}{l}

\Rightarrow \quad \frac{4}{x}=\frac{x}{25} \\

\Rightarrow \quad x^{2}=4 \times 25=100 \\

\therefore \quad x=\sqrt{100}=10 ; \text { Ans. }

\end{array}

$$

$\therefore \quad$ Correct option is $(b)$

Trick :

Mean Proportion

$$

=\sqrt{a b}=\sqrt{4 \times 25}=10 \text {; Ans. }

$$