I intend to do next generation sequencing for total six mutations in each sample. It involves 6 primer sets. In order to reduce the pipetting time can I make a stock of all primer sets in a single tube after making proper calculations?
Sure, I used to do this for three or four primers are a time for a multi-plex PCR. No reason to think it wouldn't work. Just double-check your math and use fresh stocks of each primer.
this protocol is called multiplex PCR and it's the base of the ampliseq designs from Lifetechnology. All amplicans and therefore primers need to be really specified and some rules need to be followed (https://www.thermofisher.com/blog/behindthebench/how-many-samples-can-i-multiplex-on-my-ngs-run-seq-it-out-13/).
so, yes you can mix the primers in the same tube (ampliseq uses thousands at same time).