Question

how can you distinguish between the cotton and silk on the basis of their of the burning properties of these fabrics

Answer 1

1. The fabric which burns giving a smell of burning hair will be natural silk or pure silk.
2.  The fabric which burns giving a smell of burning paper will be artificial silk.
 
Just like silk, wool is also made up of proteins. So, a piece of woollen fabric also burns giving the smell of burning hair.