the concept of admissibility is contigent upon relevancy.it is to be noted that always FACTS are relevant and EVIDENCE upon such facts are admissible.every fact which has been declared to be relevant is not always admissible.even a relevant fact is admissible only when it is proved.thus,a relevant fact might not be admissible either:-
1.when it is not proved or
2.when it is not allowed to be proved.i.e when IEA bars it proof.
for instance secs.25-26 of the indian evidence act clearly declares that confessions made to a police officer or confessions made in police custody shall not be proved.thus even if such confessions are relevant ,they are not admissible as they cannot be proved.similarly u/sec.120-130 the IEA clearly prohibits the proof of certain kinds of communications which are called priveleged communications.
other way round there are certain facts which are not expressely declared to be relevant but are allowed to be proved and thus are admissible.for instance the evidence relating to impeachment of the credit of the witness u/sec.155,though not declared to be relevant is allowed to be proved.