Explain the situations when Hearsay evidence becomes relevant?

Mainly evidence is of two types oral or documentary. Oral evidence means such evidence in which any person makes a statement orally before the court. 
Hearsay is another form of oral evidence when the oral evidence is not direct it becomes hearsay evidence. 

When any person testifies about any fact, which he himself 
1 Has not seen 
2 Has not heard 
3 Has not perceived by his senses, 
Then it is called Hearsay Evidence  

Hearsay Evidence - Hearsay Evidence is very weak evidence. It is only the reported evidence of a witness which he has not seen either heard. Sometimes it implies the saying of something which a person has heard others say. In Lim Yam Yong v. Lam Choon & Co. The Hon’ble Bombay High Court adjudged “Hearsay Evidence which ought to have been rejected as irrelevant does not become admissible as against a party merely because his council fails to take objection when the evidence is tendered.” So finally we can assert that Hearsay Evidence is that evidence which the witness has neither personally seen or heard, nor has he perceived through his senses and has come to know about it through some third person. There is no bar to receiving hearsay evidence provided it has reasonable nexus and credibility. When a piece of evidence is such that there is no prima facie assurance of its credibility, it would be most dangerous to act upon it. Hearsay evidence being evidence of that type has, therefore, to be excluded whether or not the case in which its use comes in for question is governed by the Evidence Act.

Example – Akshay says that he had received information that at the time of the accident, Bunty was driving the car. It is hearsay evidence because Akshay has not himself seen the Bunty Driving car. 
Hearsay evidence is admissible as an exception to the general rule of evidence that hearsay evidence is no evidence in the eye of law and it should be discarded as a general rule because the evidence in all cases must be direct. 
Generally, the court does not consider Hearsay evidence but here are some exceptions in which court has taken hearsay evidence into account. 
This, section thus excludes hearsay evidence. 

Exceptions to hearsay 

1 Res Gestae
Section 6 of the Act provides that the statement of a person may be proved through another person if it is so connected with the fact in issue. 

2 Admissions and confessions 
Admission and confession made outside the court may be proved by the evidence of that person who has heard it. 

3 Statements relevant under 32 
Section 32 provides that the statement of such person shall be admitted 
(a) Who has died; 
(b) Who cannot be found; 
(c) Who are incompetent to give evidence; 
(d) Whose attendance cannot be procured without an amount of delay or expense which under the circumstances of the case appears to the court unreasonable. 

4 Statements in Public Documents 
Statements written in public documents may be proved even without presenting those person who have written them. 

5 Evidence in former Proceedings 
Court proceedings can also be taken as evidence. 
6 Statement in Experts in Treatises
Section 60 contains a provision which says that the opinion of experts contained in books offered for sale, is admissible as evidence, if the author of book
(a) has died; 
(b) Cannot be found; 
(c) Is incapable of giving evidence; 
(d) His presence cannot be obtained without unreasonable delay or expense.  

7 Miscellaneous – Can the court extend these exceptions or create new exceptions? The judicial attitude appears from the speeches delivered in the House of Lords in Myers VS Director of Public Prosecution.