The polyethylene method is used for
(a) Seedless fruit production
(b) Energy production from sewage
(c) Gene transfer without a vector
(d) Biodiesel production

Hint: Polyethylene glycol can be used to perform transformation experiments without the requirement of a carrier DNA. This method is otherwise called a direct transfer method.

Complete answer:
Polyethylene glycol (PEG) is used to transfer a gene without a vector. A vector is a DNA molecule that can be used to deliver our gene of interest into the target cell. This is called an indirect gene transfer method.
PEG is utilized to induce genetic transformation in bacteria (example: E. coli) and the yeast (example: Saccharomyces cerevisiae). It can induce transformation without removing the cell wall. The transformation performed via PEG has high transformation efficiency and can yield ${ 10 }^{ 6 }-{ 10 }^{ 9 }$ transformants/µg of DNA.
It is a chemical method of DNA transformation. In this method, the protoplasts of the plants can be transformed along with the naked DNA by the PEG treatment using cations like calcium. The plasma membrane will be destabilized by PEG and the divalent cations. This destabilized plasma membrane will allow the naked DNA to enter into the cell where the DNA will get integrated into the genome of the target host.
One of the disadvantages of using PEG for the target gene transfer is that the transformed DNA will be liable to degradation. The advantage of the PEG method is that the protoplast from these plants can be separated. These protoplasts will then be used to develop into various plant parts.
So, the correct answer is, ‘Gene transfer without a vector’.

Note: There are many methods to perform vectors less transformation. These include electroporation, PEG method, microinjection, and gene gun. Electroporation makes pores in the plasma membrane and the gene will reach the nucleus. Using microinjection, the target gene can be directly injected into the genome. In the gene gun method, the gold-coated gene of interest can be bombarded into the cell so that it can reach the genome.