One of the reasons for growing inequality is "large dependency on the agriculture sector". The agriculture sector contributes to around 15% of the GDP while around 60% of the population is directly or indirectly dependent on the agriculture. remaining ~40% are dependent on secondary and service sector. As you can see, many people are dependent on the agri-sector.
While on the other hand service sector contributes around 55% of GDP while employing not many people as in agri-sector. And if you see the growth rates of these sectors, agri is growing at ~2%, secondary at ~4.4% while service sector is growing at ~8.8%.
So, it means that the lives of all these 60% of the population is more or less dependent on this 2% growth which is being divided among many people(60%) while service sector has high contribution, high growth and low population depended on, therefore their lives are better growing than in agri-sector's people.
This is one of the reasons for the lives of people depended on agriculture not getting better of which is inturn causing the inequality.
Coming to the socialist part of India, I think that when Mrs. Indira Gandhi govt made 42nd amendment to introduce "socialist and secular" in the preamble, also the DPSP avenues of socialist agenda is roughly the feeling to promote equality among standards of living of people.
"Socialist country" is a word which more or less points towards economic model of the country. India is not a socialist country, It is a capitalistic economy. I think China can be in someways called a socialistic country.