Tangent of acute angle between the curves $\mathrm{y}=\left|{\mathrm{x}}^2-1\right|$  and  $\mathrm{y}=\sqrt{7-{\mathrm{x}}^2}$ at their points of intersection is  $\lambda$ then $\left[\lambda \right]$ is_____(where [.] represents G.I.F)

$\begin{array}{l}{\mathrm{x}}^2-1=7-\mathrm{x}\\ x^4-x^2-6=0\\ \left(x^2-3\right)\left(x^2+2\right)=0\\ x=\sqrt{3}\\ \text{ The slope of tangent to }y=\sqrt{7-x^2}\text{ at the point }(\sqrt{3},2)\text{ is }\\ \mathrm{y}=\left|{\mathrm{x}}^2-1\right|\\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\left|{\mathrm{x}}^2-1\right|}{{\mathrm{x}}^2-1}\times 2\mathrm{x}=2\sqrt{3}\\ {\mathrm{m}}_2=\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-\mathrm{x}}{\sqrt{7-{\mathrm{x}}^2}}=\frac{-\sqrt{3}}{2}\end{array}$
$\begin{array}{l}{\mathrm{m}}_1={\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{(2,\sqrt{3})}=4\\ \mathrm{y}=\sqrt{7-{\mathrm{x}}^2}\\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2\sqrt{7-{\mathrm{x}}^2}}\times -2\mathrm{x}\\ {\mathrm{m}}_2={\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{\mathrm{x}=2}=\frac{-2}{\sqrt{7-4}}=\frac{-2}{\sqrt{3}}\\ \begin{array}{r}\tan \theta =\frac{{\mathrm{m}}_1-{\mathrm{m}}_2}{1+{\mathrm{m}}_1{\mathrm{m}}_2}\\ \Rightarrow \tan \theta =\frac{-5\sqrt{3}}{4}\end{array}\end{array}$

$\therefore \text{ The tangent of the acute angle between the curves is }\frac{5\sqrt{3}}{4}\text{. }$