  Let $G=\mathbb{Z}_2$ act on a finite CW-complex $X$ having mod 2 cohomology
isomorphic to the product of projective space and sphere $\mathbb{F}P^n\times
\mathbb{S}^m,$ where $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}.$ In this paper, we
have determined the connected fixed point sets and the orbit spaces of free
involutions on $X.$ As an application, we derive the Borsuk-Ulam type results.
