A modem is used for modulation and demodulation.
It converts digital signals into signals suitable for transmission and also converts received signals back into digital form.
So:
\[
A-II.
\]
An Ethernet card is a network adaptor.
It is used to connect a computer to a wired network.
So:
\[
B-IV.
\]
A repeater regenerates weak signals.
It is used to extend the distance of communication by strengthening signals.
So:
\[
C-I.
\]
A router receives data packets, analyses their destination, and forwards them to other networks.
So:
\[
D-III.
\]
Therefore, the correct matching is:
\[
A-II,\quad B-IV,\quad C-I,\quad D-III.
\]
Hence, the correct answer is option (A).