The joint equation of lines passing through origin and having slopes $(1+\sqrt{2})$ and $\frac{-1}{1+\sqrt{2}}$ is ..........

If $r$ is the radius of spherical balloon at time $t$ and the surface area of balloon changes at a constant rate $K$, then......

$$\int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \cdot \sin ^3 \theta d \theta=$$ ............

If $\omega$ is a complex cube root of unity and $A=\left[\begin{array}{ccc}\omega & 0 & 0 \\ 0 & \omega^2 & 0 \\ 0 & 0 & 1\end{array}\right]$ then $A^{-1}=\ldots$