If $x = 2^{1/3} - 2^{-1/3}$,then $2x^3 + 6x = $

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$, then the value of $\left(\frac{dy}{dx}\right)_{x=0}$ is

$RR-21$ is a high-yielding variety of:

Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$.
(iv) Repeat $(i)$,$(ii)$ and $(iii)$ for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is

Which of the following representations correctly explains the function of a mitochondrion?

Blood pressure in the pulmonary artery is