Going by the most recent Indian census data, the most commonly spoken languages are:
Hindi (57.11% of people in India can speak it; note that this includes a lot of different dialects, some of which are often considered to be their own distinct languages by many scholars as they do differ significantly)
English (10.62% - this may sound surprisingly low but consider that huge numbers of Indians live in rural areas and most of them do not speak English)
Bengali (8.88%)
Marathi (8.18%)
Telugu (7.80%)
Tamil (6.33%)
Urdu (5.22%) (Note that Hindi as popularly spoken is heavily mixed with Urdu, but this is counting speakers of pure Urdu)
Gujarati (4.98%)
Kannada (4.85)
Odia (3.52%)
Panjabi (2.98%)
Malayalam (2.94%)
Assamese (1.95%)
Maithili (1.18%)
Santali (0.64%)
Kashmiri (0.58%)
Nepali (0.28%)
Sanskrit (0.26%)
Sindhi (0.26%)
Dogri (0.23%)
Konkani (0.21%)
Meitei (0.19%)
Bodo (0.13%)
This is combining together people who speak each of these languages as their first, second, or third language. So no, there are no languages which all Indians speak fluently. India is a very linguistically diverse place.
Note that many languages appear on this map but not in the list I gave above, because many of them are sometimes counted as dialects and other times as separate languages, that distinction is not made consistently by different scholars.