how close is the india's language to english?

English is one of the official languages of India.  Some people speak it natively and many learn it as a foreign language to speak with other people.  There are many different languages spoken in India.

One of the major languages in India is Hindi.  It is distantly related to English.  They are both in the Indo-European language family, but they aren't very similar to each other. 

There are many other languages in India that are more closely to related to Hindi. 

There are languages from several different language families spoken in India. 

The Greek language, which English partly comes from, adopted many words from Sanskrit, which is used in India.  The word for 'soul' originated as the Sanskrit word, 'atman', which was translated to 'atmos' in Greek, which became the word we know in English as, 'atom'.  'Krishna' (the Jesus figure of the Bhagavad Gita), became 'Kristos' in Greek, which was translated to, 'Christ', in Aramaic, the language Jesus spoke.  

Indians seem to be very adaptable to many cultures, because their culture have had very advanced and complex systems of understanding, for thousands of years.  

There are many languages in India, but only one, Hindi, has any relationship with English, and that relationship dates back many thousands of years.

The reason so many Indians speak English is not because their language is 'close to'English. It's because India used to be a British colony, and much of the country's business was conducted in English. Even after Independence in 1947 India chose to retain English as an important working language, and it is taught in schools.

There is no "the language of India". Hindi is supported by the government but hundreds of millions don't speak it. English is used widely as Lingua Franca, but also hundreds of millions don't speak it. Then there's some two dozen other languages that are "official" and used in parts of India, and several hundred languages with less status

The two are not close. There are many Indian languages just as there are many Chinese ones.  English is taught in a number of Indian schools, so that is a major reason why many Indians can speak it.

English is an official language in India and taught in schools. Most Indians grow up speaking English as well as a native language.

Got to go a long way back to find the common language Proto-Indo-European