The longitudinal extent of India is between approximately 68°7'30" E to 97°25' E. The standard meridian of India is 82°30' E, which passes through the city of Allahabad in Uttar Pradesh. The importance of the standard meridian lies in its significance for the measurement of time and the establishment of a standard time zone for the country.

**Longitudinal Extent of India**
The longitudinal extent of a geographical area refers to the measurement of its east-west span. In the case of India, it extends from approximately 68°7'30" E to 97°25' E. This means that India covers a vast longitudinal range, spanning over 29 degrees of longitude.

**Standard Meridian**
The standard meridian is a designated line of longitude that is used as a reference point for measuring time and establishing time zones. In India, the standard meridian is located at 82°30' E, which passes through the city of Allahabad in Uttar Pradesh. This meridian was established by the Indian government to serve as a reference for the entire country.

**Importance of Standard Meridian**
The standard meridian holds great importance for various reasons:

1. **Time Measurement**: The standard meridian serves as the reference point for measuring time in India. It is considered as the starting point for calculating the Indian Standard Time (IST). The time at the standard meridian is considered as the standard time for the entire country.

2. **Time Zones**: The establishment of the standard meridian helps in dividing the country into different time zones. India has a single time zone, known as Indian Standard Time (IST), which is based on the time at the standard meridian. This ensures that time across the country is uniform and avoids confusion caused by multiple time zones.

3. **Synchronization**: The standard meridian allows synchronization of clocks and watches across the country. It ensures that people in different regions of India follow the same time, which is essential for various activities such as transportation, communication, and coordination between different regions.

4. **International Coordination**: The standard meridian also plays a role in international coordination. India's standard meridian is located at a significant distance from the Prime Meridian (0° longitude) which passes through Greenwich, London. This difference in longitude helps in determining the time difference between India and other countries, thereby facilitating international communication and coordination.

In conclusion, the longitudinal extent of India is approximately between 68°7'30" E to 97°25' E. The standard meridian of India is located at 82°30' E and holds great importance for time measurement, time zones, synchronization, and international coordination.