It is depend on your study Area. But there are some agencies providing Maps viz. Geological survey of India, NBSS& LUP for Soil, NRSC-Bhuvan for LULC...... Search
The agencies mentioned by you provide small sized poor quality maps and are crowded with text. The format is PDF sometimes. The boundary of the state never matches with that of shapefiles of the state boundary (too generalized).
In such situations developing mappers like me are facing serious problems.
As far as mapping of the Soil is concerned, your study area and its dimensions matter more, But you can prepare your own soil map with intensive field work. there is a methodology to conduct field work...
1. Prepare a physiographic map of your study area.
2. Overlay LULC and slope map on the same
3. Collect soil samples from each LULC and generalised slope Class
4. Test the samples in laboratory and interpolate the result