Explanation:

In terms of responsibilities and work with strategic importance, it is the Home Ministry is largest ministry in terms of work. 
Some of work in its Domain are:
Law and order : The issues relating to policing, its modernization, its weaponry all falls under its domain including training of IPS officers.

Intelligence : IB particularly is totally under its command. Home Ministry has the responsibility of total synergy of all Intelligence inputs from state govt. ATS to Military intelligence to RAW.

J&K : Given the strategic importance associated with J&K, home ministry is totally responsible for kashmir's Law and order situation. The amount of paramilitary forces involved in J&K, training of its police personnels.

North-east: Home Ministry also overseas North eastern policies relating to policing, Security and their stability. Its development policies with strategic importance is framed by Home Ministry.

Paramilitary Forces : paramilitary forces such as BSF, CRPF, SSB, CISF, ITBP comes directly under the purview of Home Ministry.Security of Border Regions: Its seems like this comes under army but actually its work of Home Ministry.

NSG:This elite anti-terror force for emergency situations also is a quintessential part of Home Ministry.

CBI: like other agencies this agency also belongs to HM. Central deputation of police officers and their further training.Appointment of Governor: The appointment of governors by recommendation is done by Home Ministry.