For the reaction:

 $2{\mathrm{H}}_2+{\mathrm{O}}_2⟶2{\mathrm{H}}_2\mathrm{O}, \mathrm{\Delta H}=-571 \mathrm{kJ}$

Bond energy of H-H is 435 kJ and that of O=O is 498 K. Calculate the average bond energy of O - H bond using the above data. 

Reaction  $2{\mathrm{H}}_2+{\mathrm{O}}_2⟶2{\mathrm{H}}_2\mathrm{O};\mathrm{\Delta H}=-571$ 

We know that  $∆H$(reaction) = Bond energy of reactants

bond energy of reactants- 

$$\begin{gathered} -571=2\times \text{ B.E }\left({\mathrm{H}}_2\right)+\text{ B.E. }\left({\mathrm{O}}_2\right)-2\times \mathrm{B}.\mathrm{E}(\mathrm{H}-\mathrm{O}-\mathrm{H}) \\ -571=2\times 435+498-2\times \mathrm{B}.\mathrm{E}(\mathrm{H}-\mathrm{O}-\mathrm{H}) \\ 2\times \mathrm{B}.\mathrm{E}(\mathrm{H}-\mathrm{O}-\mathrm{H})=1939 \\ 2\times \mathrm{B}.\mathrm{E}(\mathrm{H}-\mathrm{O}-\mathrm{H})=969.5 \end{gathered}$$

Bond energy of O-H bond: 

$\begin{array}{l}\mathrm{B}.\mathrm{E}.\mathrm{of} \mathrm{OH} \mathrm{bond} =\frac{969.5}{2}=484.75\cong 484\end{array}$

So, the correct answer is (a)