What examples of probable cause would allow police to enter private home without warrant?

(in India) Police Officer investigating into any offence has authority to make a search, subject to lawful authority. Whenever, the investigating officer has a reason to discover something that may work as useful evidence, and there is probability that that the accused might have utilized the particular thing, while committing the offence, the police officer has every right to so make a search even in a private home.

Another View: (in the US) If the officer(s) receive permission from the person in charge of the premises to do so - if there is contraband lying in 'plain sight' - when in 'hot pursuit' - under emergency circumstances.