Reaction between an acid and acid My initial thought was that the stronger acid will act as an acid and the weaker acid as base like the reaction between $\ce{H2SO4}$ and $\ce{HNO3}$ but in this reaction there is a lone pair available for protonation, what if the lone pair was not present , will the reaction still occur? Is the answer dependent on what the acids exactly are?
In the case of $\ce{HNO3}$ and $\ce{H2SO4}$, the proton from sulphuric acid protonates the $\ce{-OH}$ group of $\ce{HNO3}$ , which gives $\ce{NO2+}$ , $\ce{HSO4-}$ and water. 
This mixture of nitric acid and sulphuric acid is widely used as a nitrating mixture for nitration of aromatic compounds.

In case of other acid mixtures, no reaction happens, but there is an equilibrium. The stronger acids dissociates almost completely , decreasing the dissociation of the weaker one by common ion effect.