Why India fell behind China

India became an independent country in 1947. The current Chinese government was set up in 1949.

1- During the time of independence, India's industrial base was superior to China.
Source- http://marxists.kgprog.com/history/etol/newspape/ni/vol17/no02/mehta.htm

2- India had produced the first and only non-white Nobel Laureate in Science and had around 3-4 physicists whose contribution were considered to be Nobel worthy. Indian universities and colleges like Presidency College were highly regarded. China had no such universities

3-India had to face tragedies of lesser magnitude.
Comparing from 1940.
World War 2 led to the led of around 90,000 Indians directly and about 1.5 million Indians in Great Bengal Famine. The number of Chinese killed due to the war is expected to be around 20 million.
Source- http://en.wikipedia.org/wiki/World_War_II_casualties#Casualties_by_country

3- Partition killed around 0.5 million-1 million Indians (+ Pakistanis). Chinese civil war between 1946 and 1949 killed about 1.2 million people.
Source- Respective articles from wikipedia which have references

4- India's 4 declared wars (3 with Pakistan and 1 with China) led to a total of less than 20,000 casualities. Chinese participation in Korean war only led to more than 1,00,000 casualities.
Source- Respective articles in Wikipedia

5- The Great Leap Forward led to the deaths of 30-40 million people in China. There was no tragedy of similar scale in independent India

6- India inherited a highly professional and meritocratic bureaucracy from British (the ICS exams were supposedly the toughest in the world) and Independent India gave them a lot of autonomy and security of tenure. China had no such established bureaucracy, they still lack the autonomy of their Indian counterparts.

7- India always had a freer economy than China except perhaps for a small time in 1985 as indicated by EFW (Economic Freedom of the World)
Source- http://www.fnfasia.org/publications2007-detail.php?know_id=111&page_title=Latest%20Publications&county_name=Regional%20&%20International&sub_name=14

8- Some people claim that an authoritarian government is more decisive than a democratic one. History tells the reverse. My views- http://thegreatwanderer.blogspot.com/
Please read the post 'Decisiveness and democracy'

Yet today, we see that China has a per capita GDP double that of India. Its growth rate is faster. Most importantly, China has 9 universities among top 150 universities while India has none. 3 of the Chinese universities are in top 50 (all from Hong Kong).; 6 other universities in mainland China are in betwen top 50-150. India's best position is 154 and India has only 2 univeristies in top 200.
Source- http://www.usnews.com/articles/education/worlds-best-colleges/2008/11/20/worlds-best-colleges-and-universities-top-200.html

China also has much higher spend on research (as % of GDP) and the dollar-efficiency of the research in getting patents.

Articles about R&D spend and efficiency of spend in China and India.
1- http://www.financialexpress.com/news/india-lags-china-in-r&d-spending-sibal/283583/
2- http://www.mccombs.utexas.edu/news/pressreleases/konana_india_op-ed.asp