Senior Kangaroo 2023 Q6

Five cards have the numbers $101$, $102$, $103$, $104$ and $105$ on their fronts.

$101$ $102$ $103$ $104$ $105$

On the reverse, each card has a statement printed as follows:

$101$: The statement on card $102$ is false

$102$: Exactly two of these cards have true statements

$103$: Four of these cards have false statements

$104$: The statement on card $101$ is false

$105$: The statements on cards $102$ and $104$ are both false

What is the total of the numbers shown on the front of the cards with TRUE statements?