Something like a plane ticket is so easy to track.
1) There will be proof of purchase on Mrityunjay's credit card.
2) There will be a proof of purchase with the airline itself. Their records go back a few years.
3) There will be a proof of Mrityunjay checking in at the airport
4) There will be proof of Mrityunjay boarding the flight with both the airport and the airline
5) There will be proof at the destination airport that Mrityunjay landed there
6) There will be video surveillance at both airports to really prove where he was at what time.
Its as simple as that to prove to the cops that he wasn't there at the time the crime happened and there's no way Kalavati can destroy all these records.
Raghu Kaka was scared about revealing that Radha is alive so the real perpetrator doesn't attack her again.
But by submitting this proof, it will acquit Mrityunjay without revealing that Radha is alive and then he is free to look for Radha and investigate further.