The heat of neutralization of strong base and strong acid is 57.0 KJ. The heat released when 0.5 mole of ${\mathrm{HNO}}_3$  solution is added to 0.20 moles of $\mathrm{NaOH}$  solution is

The reaction of neutralization of acid and base is given below:

${\mathrm{H}}^{+}+{\mathrm{OH}}^{-}\to {\mathrm{H}}_2\mathrm{O}+\mathrm{Heat}$  

From the reaction we can say that one mole of $H^{+}$ reacts with one mole of $O{H}^{-}$ to give 57 kJ. When 0.5 moles of acid ($HN{O}_3$) reacts with 0.2 moles of base, then 0.2 moles of neutralization will take place. 0.3 moles will remain unreacted. 

$\underset{0.2 \mathrm{mole}}{{\mathrm{H}}^{+}}+\underset{0.2 \mathrm{mole}}{{\mathrm{OH}}^{-}}\to {\mathrm{H}}_2\mathrm{O}$

So, the heat evolved will be:

$Heat=\frac{57\times 0.2}{1}=11.4\text{ KJ}$ 

Therefore, the correct option is B.