In $\triangle A B C$, if $\tan A+\tan B+\tan C=6$ and $\tan A \cdot \tan B=2$ then $\tan C=$ ...........

If $P(6,10,10), Q(1,0,-5), R(6,-10, \lambda)$ are vertices of a triangle right angled at $Q$, then value of $\lambda$ is ............

For L.P.P, maximize $z=4 x_1+2 x_2$ subject to $3 x_1+2 x_2 \geq 9, x_1-x_2 \leq 3, x_1 \geq 0, x_2 \geq 0$ has

The function $f(x)=x^3-3 x$ is ............