Cloning vectors - plasmids

Reference: NCERT Class XII, page 168.

A plasmid is extrachromosomal, double-stranded, circular DNA of bacteria. So 'single-stranded' is not a feature of plasmids.

Plasmids are small, circular, extra-chromosomal DNA molecules found in bacteria (and some yeasts) that replicate independently.
They carry non-essential genes (e.g. antibiotic resistance), not genes for vital activities, and are not part of the main chromosome. They are not found in viruses.
Because they can carry foreign DNA into host cells and replicate there, plasmids such as pBR322 are widely used as vectors in gene transfer (genetic engineering).
So plasmids are widely used in gene transfer.

A plasmid is a small circular DNA that replicates independently in bacteria.
It can be cut with a restriction enzyme and a piece of foreign (e.g. eukaryotic) DNA can be joined into it with DNA ligase, forming recombinant DNA. When put back into a bacterium, the plasmid replicates and copies the foreign gene too.
Antibiotic resistance genes are useful as selectable markers, but the basic reason a plasmid is used as a vector is its ability to carry joined foreign DNA and replicate.
So, as per the answer key, plasmid is used as a vector because it is a circular DNA that can be joined to eukaryotic DNA.