Understanding Sawai Raja Jai Singh II and His Observatories

Sawai Raja Jai Singh II of Amber, a prominent Rajput ruler in the post-Aurangzeb period, was not only known for founding the beautiful city of Jaipur but also for his significant contributions to astronomy. He was keen on accurate astronomical observations and calibration of calendars. To achieve this, he constructed a series of astronomical observatories, known as Jantar Mantar.

The question states that he erected these observatories at five different places. It asks us to identify how many of the places listed in the options (Banaras, Ujjain, Mathura, Udaipur, Allahabad) were NOT among the places where he built these observatories.

Places Where Sawai Jai Singh Built Observatories

Historically, Sawai Raja Jai Singh II built astronomical observatories at the following five locations:

1. Delhi
2. Jaipur
3. Ujjain
4. Mathura
5. Varanasi (also known as Banaras)

These five observatories were equipped with large, specialized instruments designed for astronomical measurements.

Comparing the List in the Question with the Actual Locations

The question provides a list of five places: Banaras, Ujjain, Mathura, Udaipur, and Allahabad. Let's compare this list with the actual locations where Sawai Jai Singh built his observatories:

• Banaras: Yes, he built an observatory in Varanasi (Banaras). This location is on both lists.
• Ujjain: Yes, he built an observatory in Ujjain. This location is on both lists.
• Mathura: Yes, he built an observatory in Mathura. This location is on both lists.
• Udaipur: No, he did not build an observatory in Udaipur. This location is in the question's list but not among the five historical observatory locations.
• Allahabad: No, he did not build an observatory in Allahabad. This location is in the question's list but not among the five historical observatory locations.

Identifying the Places Without Observatories from the List

Based on the comparison, the places from the list provided in the question where Sawai Raja Jai Singh II did NOT erect an astronomical observatory are:

• Udaipur
• Allahabad

There are two such places.

Conclusion

Out of the five places listed in the question (Banaras, Ujjain, Mathura, Udaipur, Allahabad), Sawai Raja Jai Singh II did not erect astronomical observatories at Udaipur and Allahabad. Therefore, the number of such places is two.