The joint equation of pair of lines through the origin, each of which makes an angle of $30^{\circ}$ with Y -axis, is

Let $f(x)=\left\{\begin{array}{cc}\frac{1-\cos 4 x}{x^2} & , x<0 \\ a & , x=0 \\ \frac{\sqrt{2}}{\sqrt{16+\sqrt{x-4}}} & , x>0\end{array}\right.$ If $\mathrm{f}(x)$ is continuous at $x=0$, then the value of $a$ is

The number of solutions of $\tan x+\sec x=2 \cos x$ in $[0,2 \pi]$ is

The maximum value of the function $\mathrm{f}(\mathrm{x})=2 \mathrm{x}^3-15 x^2+36 x-48$ on the set $A=\left\{x / x^2+20 \leq 9 x\right\}$ is