Final answer:
For a straight wire of resistance R cut into quarter and three-quarter lengths, when connected in parallel, the total resistance is R/7 which is not one of the provided options. This suggests a potential error in the question.
Step-by-step explanation:
When a straight wire of resistance R is cut into two pieces from its quarter, the two resulting pieces have lengths of ¼ L and ¾ L respectively. Assuming that the resistance is uniformly distributed along the length of the wire, the resistances of these two pieces will be ¼ R and ¾ R because resistance is directly proportional to length for uniform materials and cross-sections.
When these two pieces are connected in parallel, the total resistance (Rtotal) can be calculated using the formula for the parallel combination of resistances: 1/Rtotal = 1/(R/4) + 1/(3R/4).
After calculating, we get Rtotal = R/7. Since this value is not one of the options, it indicates that the question might have been stated incorrectly or there is a typo. The correct answer, assuming no typos, would be 'none of the above'.