**Answer:**

To find the percentage increase in resistance, we need to use the formula:

Percentage increase in resistance = [(New resistance - Old resistance) / Old resistance] * 100

1. **Calculating the initial resistance:**
- The resistance of a wire is given by the formula: R = (ρ * L) / A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.
- Let's assume the initial radius of the wire is r. Therefore, the initial cross-sectional area A₁ = π * r₁².
- We are given that the wire's radius is decreased by 0.5%, so the new radius will be r₂ = r₁ - (0.5/100) * r₁ = r₁ * (1 - 0.005).
- The new cross-sectional area A₂ = π * r₂² = π * (r₁ * (1 - 0.005))².

2. **Calculating the new resistance:**
- The new resistance R₂ = (ρ * L) / A₂.

3. **Calculating the percentage increase in resistance:**
- Percentage increase in resistance = [(New resistance - Old resistance) / Old resistance] * 100 = [(R₂ - R₁) / R₁] * 100.

4. **Substituting the values and solving:**
- Let's assume the resistivity ρ and the length L of the wire remain constant.
- Substituting the values of A₁ and A₂ in the formula for R and simplifying, we get:
- R₂ = (ρ * L) / [π * (r₁ * (1 - 0.005))²].
- Substituting the value of R₂ and R₁ in the formula for percentage increase in resistance, we get:
- Percentage increase in resistance = [((ρ * L) / [π * (r₁ * (1 - 0.005))²]) - ((ρ * L) / (π * r₁²))] / ((ρ * L) / (π * r₁²)) * 100.
- Simplifying further, we get:
- Percentage increase in resistance = [(1 - (1 - 0.005)²) / (1 - 0.005²)] * 100.

By calculating the above expression, we find that the percentage increase in resistance is approximately 1%. Hence, the correct option is (a) 1%.