Among the following oxides of $3 d$ elements, the number of mixed oxides are $\_\_\_\_$ .

$$ \mathrm{Ti}_2 \mathrm{O}_3, \mathrm{~V}_2 \mathrm{O}_4, \mathrm{Cr}_2 \mathrm{O}_3, \mathrm{Mn}_3 \mathrm{O}_4, \mathrm{Fe}_3 \mathrm{O}_4, \mathrm{Fe}_2 \mathrm{O}_3, \mathrm{Co}_3 \mathrm{O}_4 $$

If the enthalpy of sublimation of Li is $155 \mathrm{~kJ} \mathrm{~mol}^{-1}$, enthalpy of dissociation of $\mathrm{F}_2$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$, ionization enthalpy of Li is $520 \mathrm{~kJ} \mathrm{~mol}^{-1}$, electron gain enthalpy of F is $-313 \mathrm{~kJ} \mathrm{~mol}^{-1}$, standard enthalpy of formation of LiF is $-594 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The magnitude of lattice enthalpy of LiF is $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest Integer)

Consider $\mathrm{A} \xrightarrow{\mathrm{k}_1} \mathrm{~B}$ and $\mathrm{C} \xrightarrow{\mathrm{k}_2} \mathrm{D}$ are two reactions. If the rate constant $\left(\mathrm{k}_1\right)$ of the $\mathrm{A} \longrightarrow \mathrm{B}$ reaction can be expressed by the following equation $\log _{10} \mathrm{k}=14.34-\frac{1.5 \times 10^4}{\mathrm{~T} / \mathrm{K}}$ and activation energy of $C \longrightarrow D$ reaction $\left(E a_2\right)$ is $\frac{1}{5}$ th of the $A \longrightarrow B$ reaction $\left(E a_1\right)$, then the value of $\left(E a_2\right)$ is

$\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest Integer)

Let $f(x)=[x]^2-[x+3]-3, x \in \mathbf{R}$, where [.] is the greatest integer funtion. Then