Background information
When electricity was introduced in India, it was still a British colony and consequently it adopted the then British plug and socket standards: type D and type M. After India had achieved independence in 1947, it continued to use these plug and socket systems. Around that time, however, the United Kingdom (and its then colonies) started the transition to a new, safer plug standard (type G), which explains why former British colonies that gained their independence a decade or more after India use the current British standard.
Type C plugs are also frequently used in India, since they often used to come with imported appliances. They are —more or less— compatible with type D sockets; the connection may be a bit unstable and sometimes unsafe, but the combination works relatively well. Because of the safety hazards, the Indian government has forbidden the import of appliances without a proper D or M plug.