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Here is a list of Indian states/UTs with predominant languages:

1. Jammu & Kashmir (Dogri, Kashmiri, Ladakhi, Punjabi, Urdu, Hindi, Baltistani, Dardi)
2. Himanchal Pradesh (Hindi, Pahadi)
3. Punjab (Punjabi, Hindi and Urdu)
4. Haryana (Hindi, Haryanvi, Predominantly Muslim - Urdu)
5. Rajasthan (Hindi, Rajasthani, Marwadi, Predominantly Muslim - Urdu)
6. Uttar Pradesh (Hindi, Brijbhasha, Pahadi, Avadhi, Bhojpuri, numerous others, Pred. Musl. - Urdu)
7. Madhya Pradesh (Hindi, Marathi, numerous others, pred. Muslim - Urdu)
8. Gujarat (Gujarati)
9. Maharashtra (Marathi, Vidarbha region - Hindi and Marathi)
10. Karnataka (Kannad)
11. Goa (Konkani)
12. Kerala (Malayalam)
13. Tamil Nadu (Tamil)
14. Lakshadweep (small chain of islands - Malayalam (?) )
15. Andaman & Nicobar Islands (Andamanese)
16. Andhra Pradesh (Telugu, Hyderabad city - Telugu plus Urdu)
17. Orissa (Oriya)
18. Bihar (Hindi, Bhojpuri, Maithini, Santhali, Angika, numerous others, Bengali, Pred. Muslim - Urdu)
19. West Bengal (Bengali)
20. Sikkim (Nepali, Lepcha, Bhutia)
21. Assam (Assamese, others)
22. Meghalaya (Garo, Khasi)
23. Arunanchal Pradesh (I plead ignorance!)
24. Mizoram (Mizo)
25. Nagaland (Naga)
26. Tripura (Tripuri, Bengali, Kuki)
27. Delhi (Capital City and sorrounding area - given quasi-statehood
recently)

Other languages - Sindhi, Sanskrit
Other Indian languages which are not represented in the "leftover" India -
Baluchi, Pashto (in Pakistan now)