1. A wire of resistance \( R \) and length \( L \) is cut into 5 equal parts. If these parts are joined in parallel, then the resultant resistance will be:

Explanation:
1. Resistance of each part: The resistance of a wire is directly proportional to its length (\( R \propto L \)). When the wire is cut into 5 equal parts, the length of each part becomes \( L/5 \). Therefore, the resistance of each part will be \( r = \frac{R}{5} \).

2. Parallel Combination: When these 5 identical parts, each of resistance \( \frac{R}{5} \), are connected in parallel, the equivalent resistance (\( R_{eq} \)) is given by the formula:
\( \frac{1}{R_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3} + \frac{1}{r_4} + \frac{1}{r_5} \)

3. Calculation:
\( \frac{1}{R_{eq}} = \frac{5}{R} + \frac{5}{R} + \frac{5}{R} + \frac{5}{R} + \frac{5}{R} \)
\( \frac{1}{R_{eq}} = \frac{25}{R} \)
\( R_{eq} = \frac{R}{25} = \frac{1}{25} R \)

Hence, Option A is the correct choice.