To which group does the $HIV$ virus belong?

Which of the following is a mode of transmission for $HIV$?

How many of the following statements regarding the transmission of $AIDS$ are correct?
$(a)$ $AIDS$ is transmitted by using the belongings of an infected person.
$(b)$ It can be transmitted through organ transplantation.
$(c)$ It can be transmitted through blood donation.
$(d)$ It can be transmitted from mother to child through the placenta.
$(e)$ It spreads through droplet infection via sneezing and coughing.
$(f)$ It is transmitted from a breastfeeding mother to her child.
$(g)$ It can be transmitted through the saliva of a patient.

Which of the following can be considered as the factory of $HIV$?

Assertion: $HIV$ infected persons are prone to opportunistic diseases.
Reason: Immune system weakens during $HIV$ infection.

$A$ doctor while operating on an $HIV$ positive patient accidentally cuts himself with a scalpel. In order to confirm whether he has contracted the virus,which of the following tests should be performed?