If $0 < y < 2^{1/3}$ and $x(y^3 - 1) = 1$,then $\frac{2}{x} + \frac{2}{3x^3} + \frac{2}{5x^5} + \dots = $

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is

Consumption of which one of the following foods can prevent the kind of blindness associated with vitamin-$A$ deficiency?

Name the method of asexual reproduction in lichens.

The major product in the following reaction is:

$A$ $Ge$ specimen is doped with $Al$. The concentration of acceptor atoms is $\sim 10^{21} \text{ atoms}/m^3$. Given that the intrinsic concentration of electron-hole pairs is $\sim 10^{19} /m^3$,the concentration of electrons in the specimen is: