I read the following line in NYT:
A surging crowd near a Hindu temple killed at least ten people and injured 25 others in the eastern Indian state of Jharkhand on Monday, police said.
Now, my questions regarding this line are:
An editor might prefer eastern Indian here to avoid any potential confusion with other meanings of East Indian; East India has several meanings, and East Indian can also be taken as the adjectival form of the East Indies.
As to why East India or Eastern India might generally prevail, the answer is simply that there is no reliable rule for such things. Once a direction has been incorporated into a name for a specific region (e.g. the North of England vs. Northern Ireland vs. North London), whichever form has become popular tends to stick. Names are idiosyncratic, and must be looked up individually.
Regarding the larger question of when it is appropriate to say east or eastern, very broad uses are covered in articles like East or eastern; north or northern? from Cambridge's English Grammar Today or indeed at EL&U, When is the use of “north” more appropriate than “northern” and vice versa?. But once a directional descriptor has become part of the name, it need not reflect those patterns at all.
Consider, for example, that the southwestern corner of the state of Texas is generally known today as West Texas.
In contrast, the ten southernmost counties of California are almost invariably Southern California:
As you can see, the generic descriptor western Texas was once more prevalent, but when the region gained a name, it was West Texas instead of Western Texas, and so we now refer to those parts of western Texas as West Texas. Why that became the name, whereas South California languishes in post-partition fantasy maps and the odd Simon & Garfunkel lyric, is anyone's guess. We might as well ask why we say South of France but not South France, or why Los Angeles has a Westside but Manhattan only a West Side, or why people cross from North Africa or northern Africa to Southern Europe or southern Europe, but not to South Europe.
Now, East India does appear to be the name of the general region as favored by the Ministry of Tourism, for example; Wikipedia uses this name as well. The adjectival form, one would expect, would be East Indian, and we've established that names don't necessarily follow rules or patterns we expect from common nouns.
Most people not familiar with the Republic of India's political geography, which I venture to say includes most English-speakers outside of South Asia, may not be aware that East India represents a specific region of the modern state of India. Students may associate it with a certain company or one of its various European counterparts. Older or more literary types may think it refers to the East Indies, a colonial-era term for South and Southeast Asia, and especially for the islands between and including Sri Lanka and the Philippines. (The Indies stand in contrast to the West Indies in the Caribbean Sea, an extension of the same Columbian error that gave us the label "American Indians.")
To refer to Jharkhand as an eastern Indian state thus avoids any complications that east Indian might be taken as the ambiguous East Indian, and subsequently pictured somewhere in Indonesia or Malaysia, or perhaps populated by some Catholic Mumbaikars.
If you are talking about large areas, you'd use northern, southern, eastern and western (without capital letters)
http://dictionary.cambridge.org/grammar/british-grammar/east-or-eastern-north-or-northern
In American English, "East Indian" refers to the Indian subcontinent. It can be an adjective. When used as a noun, it refers either to a person from the Indian subcontinent, or to a person descended from people from the Indian subcontinent.
"East Indian" contrasts with "American Indian". "American Indian" can be used as an adjective. When used as a noun, it refers to a person descended from the inhabitants of North America and/or South America before the arrival of Christopher Columbus.
If the context is clear, both "East Indian" and "American Indian" can be shortened to "Indian". When "East Indian" is shortened to "Indian", it usually refers to India (not Pakistan or Bangladesh).
