Question

the number of c-c sigma bonds present in 1-butyne is

Answer 1

It's very simple: 
a single bond is a sigma bond 
a double bond is 1 sigma bond + 1 pi bond 
a triple bond is 1 sigma bond + 2 pi bonds 

If you're only interested in the number of sigma bonds, that number is equal to the number of single bonds. 

If you draw 1-butyne, you count 3 C-C single bonds.
so it will have 3 C-C sigma bonds.


Simple enough?

i hope its clear now?