What can be obtained from somatic hybridization?

Let $a, b, c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8 x)(ax^2 + bx + c) dx = \int_{0}^{2} (1 + \cos^8 x)(ax^2 + bx + c) dx$. Then the quadratic equation $ax^2 + bx + c = 0$ has:

Which of the following exhibits the weakest intermolecular forces?

$A$ capacitor is charged by using a battery,which is then disconnected. $A$ dielectric slab is then inserted between the plates. What is the result?

If a point $(x, y) = (\tan \theta + \sin \theta, \tan \theta - \sin \theta)$,then the locus of $(x, y)$ is

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively $\rho_1$ and $\rho_2$. The ratio of the accelerations due to gravity at their surfaces is