Dear Student,
a. In a Parliamentary democracy, President is the head of the state who represents the country and Prime Minister is the head of the government. The real executive powers are vested with the Prime Minister and his Council of Ministers.
b. Though we do not have direct elections for Prime Miniter, he is the leader of the majorty party in the Lok Sabha which is directly elected by the people. That is why the Prime minister is the real executive head.
c. The President appoints the leader of the party as Prime Minister that commands majority in the Lok Sabha.
d. The Prime Minister has to be the member of either the Lok Sabha or Rajya Sabha.
e. . In case no single party or alliance gets a majority, the President appoints the person most likely to secure a majority support.
f. Prime Minister is elected for a period of five/5 years, he can be re elected if his party is voted in power in the next General elections.
Regards