Yes, India needs to have more than one standard time, because there is a time gap of about 2 hours between the easternmost parts to westernmost parts to westernmost parts of the country. The large longitudinal expanse of India about 30°  approximately. So even when the sun is still shining in the western coast, it is already night in the northeast. Hence, we need two or three time zones to clearly reflect diurnal changes.

A country like USA has seven times zones due to their vast east to a west extent.