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$82\dfrac{1}{2}^\circ E$ longitude is geographically significant to India because__________.
A)It determines the Indian Standard Time
B)It has a bearing on the tropical climate of India
C)It divides India into eastern and western zones
D)It enables determining local time in eastern India

Answer
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Hint: To, have a clear description of a certain area or part of Earth’s surface, Longitude and latitude help. Longitudes are the imaginary line that is marked from the north to south direction. The local time of places that lie on the different meridians differ

Complete answer:
The lines of longitude change as the Earth revolves from west to east direction from the prime meridian. The Longitude meets at poles and they cross the equator at right angles.
Every country has its central meridian to have the local time; they calculate their own country's time. Based on one hour each earth is divided into two-four parts, each part covers 15 percent of longitude.

In India, local time calculated by the longitude is known as has Indian Standard Time (IST), here this IST is calculated based on the longitude which crosses a clock tower in Mirzapur with $25.15^\circ N$ and $82.58^\circ E$ which is located near Allahabad in Uttar Pradesh state.

$82\dfrac{1}{2}^\circ E$ longitude is geographically significant to India because it decides the Indian Standard Time (IST) which is chosen as India’s Standard Meridian as is present in the center of all longitudes and latitudes of India. Sri Lanka and India have the same local time. Some countries have 2 local times as they have a greater longitudinal extent.

Hence, the correct answer is option (A)

Note: India Standard time adds 5 hours 30 minutes with Coordinated Universal Time (UTC), this standard time is set as the sun rising in the state of Arunachal Pradesh will be two hours earlier compared to Gujarat, so to avoid confusions this standard time is calculated.