Human Health and Disease

Retroviruses (e.g. HIV, and oncogenic viruses such as HTLV) have RNA as their genetic material in the mature virus particle; true.
They carry the gene for the enzyme reverse transcriptase (RNA-dependent DNA polymerase); true.
Inside the host cell, reverse transcriptase copies the viral RNA into DNA. This viral DNA integrates into the host genome as a provirus and is then transcribed to make new viral RNA. So DNA is definitely present at one stage of the life cycle.
Some retroviruses cause certain kinds of cancer in humans (e.g. HTLV-1 causes T-cell leukaemia); true.
So the statement that is not true is: DNA is not present at any stage in the life cycle of retroviruses.

Cancer cells have lost the normal controls on cell division (contact inhibition), so they divide rapidly and continuously.
Cells are most sensitive to radiation while they are dividing, because their DNA is being replicated and the chromosomes are condensing; radiation damage to DNA at this time stops division and kills the cell.
So radiotherapy damages rapidly dividing cancer cells more than normal cells, most of which divide slowly or not at all. (This is also why rapidly dividing normal cells, such as those of hair follicles and bone marrow, are affected during radiotherapy.)
So cancer cells are more easily damaged by radiation because they are undergoing rapid division.

Culex mosquito transmits Wuchereria bancrofti, which causes filariasis (elephantiasis); correctly matched.
Aedes aegypti transmits the viruses of yellow fever (and dengue); correctly matched.
Glossina palpalis (tsetse fly) transmits Trypanosoma, which causes African sleeping sickness; correctly matched.
Anopheles culicifacies is a vector of malaria (Plasmodium). Leishmaniasis (kala-azar) is transmitted by the sandfly Phlebotomus, not by Anopheles.
So the pair that is not correctly matched is Anopheles culicifacies – Leishmaniasis.