You have asked the duties of Secretary and Deputy Secretary to Government of India.
In this reference I want to mention that there is one Cabinet Secretary, two Secretaries, one Additional Secretary and one Joint Secretary assisting to Government of India.
The Cabinet Secretary is the coordinator for all the activities related to policies and administrative work and also works for council of Ministers.
One Secretary looks after coordination and public grievances. The other Secretary takes care of security and security issues.
Additional Secretary takes care of work related to cabinet committees, secretariat meetings, parliament questions etc.
Joint Secretary is responsible for coordination between ministries, vigilance, work related to government rules etc.
Deputy Secretary takes care of holding meetings, exercising delegated powers of head of offices, coordination with PSUs etc.
The above information is the brief of the duties of Secretaries in government. If you are interested to know something in more detail I advise you to have a look at the government site - http://cabsec.nic.in
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