If there is a trojan on my computer, can it go undetected by my Anti-Virus software?

I have KasperSky Anti-Virus.

Virus or Trojans have many variants and some security programmes are up to date and some or not. The software vendor will update the definitions every time when they find any new variants and if the database of you antivirus was not updated in a regular then your antivirus shields will not aware of the new variants.

That is why there is a need of updating the virus definitions and some free editions will not have the in-depth virus signature files and there will be alot of difference in the free version and full version of software's.

Because I observed many free antivirus programmes that do not have full feature they don't detect the antivirus and then I installed a Trojan Remover trial version which I was benefited from it alot it detected alot threats where in as antivirus cannot.

So I come to know that a full version of antivirus works better than free version and so I suggest you to install the full version of antivirus it's better and so many links are available on the Internet and they say that are full version but one thing you need to they don't have official support from the software provider.