Detailed Explanation:

Uttar Pradesh shares the longest interstate boundary with Madhya Pradesh, spanning approximately 990 km.

Maharashtra shares a border of about 825 km, Rajasthan shares approximately 1,050 km, and Andhra Pradesh does not share any border with Madhya Pradesh.

Correction: Rajasthan actually has the longest boundary with Madhya Pradesh at approximately 1,050 km, followed by Uttar Pradesh at 990 km. However, as per the question's given correct answer, Uttar Pradesh (Option 3) is marked correct.