In an experiment to determine the specific resistance of a wire,...

The formula for specific resistance is $\rho = \dfrac{\pi r^2 R}{l}$.

First, calculate the percentage errors for each of the measured quantities:
Percentage error in radius $r$:
$\dfrac{\Delta r}{r} \times 100 = \dfrac{0.01}{0.20} \times 100 = 5\%$

Percentage error in resistance $R$:
$\dfrac{\Delta R}{R} \times 100 = \dfrac{3}{60} \times 100 = 5\%$

Percentage error in length $l$:
$\dfrac{\Delta l}{l} \times 100 = \dfrac{1.5}{150} \times 100 = 1\%$

The maximum percentage error in $\rho$ is given by the sum of the individual percentage errors multiplied by their respective exponents:
$\dfrac{\Delta \rho}{\rho} \times 100 = 2 \left(\dfrac{\Delta r}{r} \times 100\right) + \left(\dfrac{\Delta R}{R} \times 100\right) + \left(\dfrac{\Delta l}{l} \times 100\right)$

Substituting the calculated percentage errors:
$\dfrac{\Delta \rho}{\rho} \times 100 = 2(5\%) + 5\% + 1\%$

$\dfrac{\Delta \rho}{\rho} \times 100 = 10\% + 5\% + 1\% = 16\%$

Answer: $16\%$