Step 1: Understanding the Concept:
Indian maritime geography and coastal baseline lengths: Goa possesses the shortest mainland coastline among coastal states at approximately 101--104 km.
Key Formula or Approach:
\[ \text{Mainland Coastline Lengths: Goa } (\approx 101\text{ km}) < \text{Karnataka } (300\text{ km}) < \text{Odisha } (480\text{ km}) < \text{Gujarat } (1600\text{ km}) \]
Step 2: Detailed Explanation:
In Indian maritime geography and coastal fisheries administration:
- India has a total mainland coastline of $6,100\text{ km}$ (and $7,516.6\text{ km}$ including island territories) spanning 9 coastal states and 4 union territories:
1. Minimum Coastal Length (Shortest): Goa (A) with a coastal length of only approximately 101 km (mainland).
2. Maximum Coastal Length (Longest): Gujarat with approximately 1,600 km ($24\%$ of national coastline), followed by Andhra Pradesh ($974\text{ km}$) and Tamil Nadu ($906.9\text{ km}$).
- (Karnataka has $300\text{ km}$; Odisha has $480\text{ km}$).
Step 3: Final Answer:
Therefore, the Indian state with minimum coastal length is Goa, corresponding to option (A).