Which city lies on India’s Standard Meridian at ${82}^{°}{30}^{\prime }E$?

The correct option is Mirzapur.

Step-by-Step Explanation:

1. Understanding the Standard Meridian of India:
India is a vast nation stretching longitudinally from approximately 68° 7' E to 97° 25' E. Because of this wide longitudinal extent of about 30 degrees, there is a local time difference of nearly two hours between easternmost Arunachal Pradesh and westernmost Gujarat. To prevent confusion and maintain time uniformity throughout the nation, a central longitude was chosen as the Standard Meridian of India.

The longitude chosen for India's Standard Meridian is:

${82}^{°}{30}^{\prime }E$

2. Location of the Meridian:
This meridian line passes right through Mirzapur in Uttar Pradesh (located near Prayagraj / Allahabad). The local civil time along this meridian is officially adopted as the Indian Standard Time (IST) for the whole country.

3. Relation to Greenwich Mean Time (GMT):
Because Earth rotates 360° in 24 hours (or 1° every 4 minutes), the longitude of 82.5° E places Indian Standard Time exactly 5 hours and 30 minutes ahead of Greenwich Mean Time (GMT + 5:30).