Equal volumes of 0.1M ${\mathrm{AgNO}}_3$ and 0.2M $NaCl$ solutions are mixed. The concentration of nitrate ions in the resultant mixture will be

$M_1{V}_1=M_2{V}_2$

$\underset{0.1\mathrm{M}}{{\mathrm{AgNO}}_3}+\underset{0.2M}{\mathrm{NaCl}}\to \underset{0}{AgCl}+\underset{0 }{NaN{O}_3}$

AgNO₃ is limiting reagent

$$\begin{gathered} \underset{0.1\mathrm{M}}{{\mathrm{AgNO}}_3}+\underset{0.2M}{\mathrm{NaCl}}\to \underset{0}{AgCl}+\underset{0 }{NaN{O}_3} \\ 0 0.1\mathrm{M} 0.1\mathrm{M} 0.1\mathrm{M} \end{gathered}$$

After reaction 0.1M NaNO₃ is formed it ionises in solution 

$$\begin{gathered} {\mathrm{NaNO}}_3\leftrightharpoons {\mathrm{Na}}^{+}+{\mathrm{NO}}_3^{-} \\ 0.1\mathrm{M} 0.1\mathrm{M} 0.1\mathrm{M} \end{gathered}$$

$\left[{\mathrm{NO}}_3^{-}\right]=\frac{0.1}{2}=0.05\mathrm{M}$