The correct answer is option 2, Allahabad. Maharaja Sawai Jai Singh of Jaipur had built the famous observatories known as Jantar Mantar in multiple locations. These observatories were used for astronomical observations and calculations. However, he did not build an observatory in Allahabad. The other options - Varanasi, Ujjain, and Mathura - are incorrect as well because Maharaja Sawai Jai Singh did build observatories in these places. In Varanasi, the Jantar Mantar observatory is known as Man Mahal. In Ujjain, it is called Vedh Shala, and in Mathura, it is known as Yantra Mandir. Therefore, the correct answer is option 2, Allahabad, where Maharaja Sawai Jai Singh did not build an observatory.