The use of the word "India" as a singular polity was a choice made by our former colonial master.  The name "India" found general agreement among the leaders of the new republic, who not so coincidentally, were also overwhelmingly from the northern parts of India. 

See also: https://en.wikipedia.org/wiki/India#Etymology

The Concise Oxford Dictionary of Linguistics by PH Matthews distinguishes Indic scripts from the Dravidian scripts, clearly specifying that Indic refers to the languages belonging to the Indo-Aryan Family (see page 175 of 410)

Text reproduced below:

Indian scripts . Writing systems derived directly or indirectly from the ^*Brahmi script, attested in ancient India from the second half of the 1st millennium BC. Modern forms include ^*Devanagari, used in particular for Hindi, and the separate scripts, often with characters of very different shapes, that have developed for other major^*Indo-Aryan and for the ^*Dravidian languages: in addition, those of ^*Tibetan, and of most languages in South-east Asia, including ^*Burmese, ^*Khmer, ^*Lao, and ^*Thai. Earlier forms were used still more widely, in Central Asia with the spread of Buddhism and e.g. for ^*Javanese before the Muslim conquest.

The basic type is ^*alpha-syllabic, as ^*Devanagari. The precise historical links, both within and outside ,are still partly uncertain: but for those in South-east Asia, the Mon script, attested in Burma ( Myanmar) from the 11 th to the 12th century AD, and before it the Grantha script, used in the coastal area of Tamil Nadu from the 5th century AD, were major intermediaries.

Indic = Indo-Aryan.

(Source: http://www.questia.com/read/55186560/the-concise-oxford-dictionary-of-linguistics)

Kind Regards,

Anirudh