Explanation:

Let's analyze the historical location of the Lion Capital of Ashoka. \nOption A: Prayagraj (formerly Allahabad) is a historically significant city in Uttar Pradesh, known for the Triveni Sangam. While it has Ashokan pillars, the specific Lion Capital that serves as India's national emblem was not found here. Therefore, Prayagraj is incorrect. \nOption B: Sarnath, located near Varanasi in Uttar Pradesh, is where the original Lion Capital of Ashoka was erected around $250 \text{ BCE}$. This iconic sculpture, depicting four Asiatic lions standing back to back on an elaborate base that includes other animals and a dharma chakra, was discovered in the ruins of the Sarnath temple. It is now preserved at the Sarnath Museum, and its design forms the basis of the National Emblem of India. This is the correct location. \nOption C: Mathura is an ancient city in Uttar Pradesh, known for its rich cultural and religious history, particularly its association with Lord Krishna and as a center for Mathura school of art. However, it is not the site where the Lion Capital of Ashoka was originally found or is currently housed. Therefore, Mathura is incorrect. \nOption D: Aligarh is a city in Uttar Pradesh, primarily known for Aligarh Muslim University. It does not have any historical association with the Lion Capital of Ashoka. Therefore, Aligarh is incorrect. \nThus, the Sinh Stambh, which is the Lion Capital of Ashoka and serves as the National Symbol of India, is situated in Sarnath.