It's a myth that countries grow and that unequal growth is somehow pathalogical. Generally, a few people in a small area start growth, which then feeds into the economy as a whole. Trickle-down does in fact work, which is why the poorest decile of a rich country is much better off than the richest decile in a poor country. When the relevant area to figures out growth coincides with the political grouping--say in Botswana or Hong Kong or Mauritania--we say that the country is getting richer. When that area is inside of a larger political unit, we say that there are regional disparities.
And so you have the well-chronicled fact that India's growth is regionally unbalanced. This is often sold as the claim "western and southern states do well" but there's a bit more to it. This map (blue and red are good, brown and yellow bad) is a little dated--from the 1991 census--and so does not capture recent unequal growth, but does look at some measure of development at a district level.
One thing to note is that the landlocked northern "bimaru" states in the Hindi belt--Bihar, Madhya Pradesh, Rajasthan, Uttar Pradesh are not doing so great. Most inland areas in general are doing fairly poorly as well. Development is largely clustered into two sets of districts: Those near the coast and those along the far northern Delhi-Punjab corridor. Of course, there are some cities here and there that do well, and the whole of Maharashtra appears well-run. Coastal Andhra and Orissa are not uniformly great, but those two states have made a lot of progress in the last fifteen years not seen on the map.
This disparity is a little striking as northern India was for a long time the richest portion of India. It was the seat of the Mauryan, Gupta, and Mughal Empires and home to the British Raj. This wealth persisted even after independence.
Political mismanagment goes a long way towards explaining this gap: National Congress rule tried to eliminate regional imbalances, which involved neglecting the richer states. On the state level, coastal and far Northern states are simply run better than those in the center. Geographical size seems to matter, as smaller states tend to be better run, while the bimaru states are all massive (Though Maharashtra is rather large as well). This was the rationale for breaking off some states from the larger ones, a policy that seems to have worked rather well.
You also have to wonder if being landlocked is a curse, as per Sachs and Collier. State-level variation in GDP in America does not seem to be especially correlated to distance from the coast, but that also reflects massive investments in infrastructure that reduce transportation costs. Those inland states in India that got rich did so by exporting crop surpluses on highways and railways.
Increasing the ties betwen inland India--which includes the bimaru states as well as rural portions of coastal states--into the part of India which is growing rapidly is obviously important. It's also essential to tapping into India's "demographic divididend"--India's relatively youthful workforce. It turns out that this bonanza is largely expected in the high-fertility bimaru states--which already contain about 40% of India's population between them. For labor-intensive industry to take advantage of these workers, inland states will need to be as investment-ready as coastal states. Otherwise, the rich parts of India will see large wage inflation and the poorer parts significant unemployment.
Massive investments in human capital and infrastructure are necessary to close this gap, and accountable governance in smaller states is the way there. Plans for a freight corridor between Delhi and Mumbai along Tokyo-Osaka lines are promising, and the Golden Quadrangle linking major Indian metros is working well. Another corridor from Delhi to Calcutta along the Grand Trunk Road could hit another quarter of the population.