$\mathrm{Zn}$ gives $\mathrm{H}_2$ gas with $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{HCl}$ but not with…
$\mathrm{Zn}$ gives $\mathrm{H}_2$ gas with $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{HCl}$ but not with $\mathrm{HNO}_3$ because:
$\mathrm{Zn}$ acts as an oxidizing agent when reacts with $\mathrm{HNO}_3$
$\mathrm{HNO}_3$ is weaker acid than $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{HCl}$
in electrochemical series $\mathrm{Zn}$ is above hydrogen
$\mathrm{NO}_3^{-}$is reduced in preference to hydronium ion
Solution
Nitric acid $\left(\mathrm{HNO}_3\right)$ is a strong oxidising agent. The Hydrogen gas produced during its reaction with metal gets oxidised to $\mathrm{H}_2 \mathrm{O}$, hence no hydrogen gas is produced.
Usually when $\mathrm{Zn}$ reacts with acid, it acts as a reducing agent which gets oxidised to a salt and the acid is the oxidising agent which gets reduced to hydrogen gas.