If the DNA of a virus is labelled with ${}^{32}P$ and the protein of the virus is labelled with ${}^{35}S,$ after transduction which molecules would be present inside the bacterial cells?

The correct option is A ${}^{32}P$ only
If DNA of virus is labelled with ${}^{32}P$ and protein of virus is labelled with ${}^{35}S,$ then after transduction, radioactive ${}^{32}P$ could be present in bacterial cells as DNA is responsible for transfer of any character in next generation and not proteins. DNA has phosphorous (P) as its contituents and hence ${}^{32}P$ will be present inside the bacterial cells as only DNA is transferred in transduction from virus to bacteria.