Well.... the text book answer will be there is no REAL executive head in a parliamentary government, since parliamentary government doesn't really follow the strict "Separation of Powers" structure. read more
In the parliamentary system of government provided by the Constitution, the President is the nominal executive authority (de jure executive or titular executive or constitutional head) and Prime Minister is the real executive authority (de facto executive). read more
Basically Indian parliamentary system has 2 heads one being the head of the state( also country or nation ) which is the President who is the nominal (de jure executive) and the other one is the Prime Minister who is the real executive (de facto executive). read more
The council of ministers or the cabinet exercises the real executive powers and authority to run the Government. In many countries, the Prime Minister is the the head of the council of ministers. The Parliamentary or the Cabinet system originated in England. This form of government exists in countries like Britain, India and Canada. read more