What can be obtained from somatic hybridization?

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

Fossil $X$ is older than fossil $Y$ if

The values of $t$ such that the matrix $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & t \\ 4 & 7-t & -6 \end{bmatrix}$ has no inverse,are

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by:

The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0$ for $x>0$ is equal to