Question

What is the reason behind taking 82 degree 30 mins. as the standard meridian of India??

Answer 1

 It is close to the middle of the country (east-west). Also, it is a multiple of 7.5 degrees (half-hours) from the Greenwich meridian. Using 75 degrees E would be to far to the west, and using 90 degrees E would be too far to the west. Using 83.5 degrees E results in a nice 5.5 hour offset from London time.