The correct option is 1 and 3 only.
Explanation
The Indian Standard Time (IST) is determined by a specific longitude known as the Standard Meridian. This meridian synchronizes clocks across the country relative to the Prime Meridian (Greenwich Mean Time).
Statement 1 is Correct: The Standard Meridian of India is 82°30' E. This longitude passes through Mirzapur (near Prayagraj/Allahabad) in Uttar Pradesh and is used to set the uniform time for the entire country.
Statement 2 is Incorrect: According to international convention, standard meridians are generally selected in multiples of 7°30' of longitude, not necessarily 15°. A span of 7°30' corresponds to a time difference of 30 minutes. Since 82°30' is a multiple of 7°30', it allows the time difference to be expressed in half-hour units relative to GMT.
Statement 3 is Correct:
Indian Standard Time (IST) is ahead of Greenwich Mean Time (GMT) by 5 hours and 30 minutes. This is calculated based on the earth's rotation rate of 1° in 4 minutes:
82.5° × 4 minutes = 330 minutes = 5 hours 30 minutes.
Key Takeaway: India utilizes a single time zone based on the 82°30' E meridian, which is chosen as a multiple of 7°30' to ensure a convenient time offset of +5:30 from GMT.