If $\cos x + \cos^2 x = 1$,then the value of $\sin^2 x + \sin^4 x$ is

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} ~kg ~m^{-1}$ is represented by the equation $y=0.2 \sin (1.5 x+60 t)$,where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

Which of the following is less general in characters as compared to genus?

The Gibbs energy for the decomposition of $Al_2O_3$ at $500^o C$ is as follows :
$\frac{2}{3} Al_2O_3 \rightarrow \frac{4}{3} Al + O_2, \Delta G = +966 \ kJ \ mol^{-1}$
The potential difference needed for electrolytic reduction of $Al_2O_3$ at $500^o C$ is at least ...... $V$.

Explain the reason for the fusion of an organic compound with metallic sodium for testing nitrogen,sulphur and halogens.

Two concentric hollow spherical shells have radii $r$ and $R$ $(R \gg r)$. $A$ charge $Q$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is