In one political system the head of the state exercises only nominal power evaluate the statement and mention any 3 situation the P. M use his discrision power.
Answers
Every successful constitution make sure the concept called Balance of Power. President is one of such post who make sure that legislative and executives work as per constitution.
Though lot of people call President of India as Rubber Stamp, which is not actually true.
President can always question the recommendation of PM and council of ministers. ( As per article 74 of Indian constitution)
President has different Veto powers to exercise over acts of Parliament if that acts are not good for citizens of India.
President also controls the state acts if governor feels, decision to be taken from President. President has all the rights to reject entire act if he feels that is not good for the society.
Note that none of the constitutional amendments can be made without the signature of President.
President appoints 2 Anglo Indians for Loka sabha, 12 MP's for Rajya sabha, Governess, Supreme court and High court judges, CAG, calling for joint sitting of Parliament etc. though for some these appointments, President is bound to PM and others.
Also President has some discretionary powers to make sure that government works as per constitution.
Considering all these points President of India is very much essential for safe running of government as per the constitution of India. Though he doesn't make his action by his own in most of the cases, he acts as checking point of actions taken by others.