A certain quantity of real gas occupies a volume of $$0.15~ \mathrm{dm}^{3}$$ at $$100 \mathrm{~atm}$$ and $$500 \mathrm{~K}$$ when its compressibility factor is 1.07 . Its volume at 300 atm and $$300 \mathrm{~K}$$ (When its compressibility factor is 1.4 ) is ___________ $$\times 10^{-4} ~\mathrm{dm}^{3}$$ (Nearest integer)
$$\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB} . \Delta H_{f}^{0}=-200 \mathrm{~kJ} \mathrm{~mol}^{-1}$$
$$\mathrm{AB}, \mathrm{A}_{2}$$ and $$\mathrm{B}_{2}$$ are diatomic molecules. If the bond enthalpies of $$\mathrm{A}_{2}, \mathrm{~B}_{2}$$ and $$\mathrm{AB}$$ are in the ratio $$1: 0.5: 1$$, then the bond enthalpy of $$\mathrm{A}_{2}$$ is ____________ $$\mathrm{kJ} ~\mathrm{mol}^{-1}$$ (Nearest integer)
$$25.0 \mathrm{~mL}$$ of $$0.050 ~\mathrm{M} ~\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$$ is mixed with $$25.0 \mathrm{~mL}$$ of $$0.020 ~\mathrm{M} ~\mathrm{NaF} . \mathrm{K}_{\mathrm{Sp}}$$ of $$\mathrm{BaF}_{2}$$ is $$0.5 \times 10^{-6}$$ at $$298 \mathrm{~K}$$. The ratio of $$\left[\mathrm{Ba}^{2+}\right]\left[\mathrm{F}^{-}\right]^{2}$$ and $$\mathrm{K}_{\mathrm{sp}}$$ is ___________.
(Nearest integer)
The area of the region enclosed by the curve $$f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi$$ and the $$x$$-axis is