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Yes, it is true due to Revolution when sun rises in east India it is still night in its western parts but for few minutes.
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Well yes it would yet be night time in the gujrat when the sun rises in the arunachal pradesh because : 
1. there is a difference of longitude from place to place and because of this there would be difference. But the time would remain the same because we are following the Indian Standard Time. 

2. The movement of the the earth i.e from west to east is also the reason for this kind of difference. 

3. It takes around 3-4 minutes for the light to travel from the one place to other. therefore there is this kind of difference. 
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