Option 1: This option states that all viruses contain a core of RNA. However, this is not true for all viruses. While many viruses do contain RNA as their genetic material, there are also viruses that contain DNA. So, this option is false.

Option 2: This option states that all viruses can infect bacteria. This is true. Bacteriophages are viruses that specifically infect bacteria, causing them to replicate and eventually lyse (burst).

Option 3: This option states that viruses cannot produce antibodies. This is true because viruses are not capable of producing their own antibodies. Antibodies are produced by the immune system of the host in response to viral infection.

Option 4: This option states that all viruses can multiply only in host cells. This is true. Viruses are obligate intracellular parasites, which means they require a host cell to replicate and multiply. They use the host cell`s machinery to produce more viral particles.

In conclusion, the correct answer is option 4.