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Strategic location and a good hold on Bay of bengal. Situated on a plain with varied resources. Good moderate climate attracted people.
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Both Bihar and UP have been the most populous state since ancient times.  At the same time the population has grown faster than the rest of the country in the last few decades. 
Chart 1 shows the comparative population growth rate of UP, Bihar and whole of India (including UP and Bihar). Combine this with the huge population of these two states and one can easily get the reason why these two states are so densely populated. 

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