If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ $(a > b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

Which of the following is not true for glucose?

The $emf$ (in $V$) of a Daniell cell containing $0.1 \ M$ $ZnSO_4$ and $0.01 \ M$ $CuSO_4$ solutions at their respective electrodes is
$(E_{Cu^{2+} / Cu}^{\circ} = +0.34 \ V; E_{Zn^{2+} / Zn}^{\circ} = -0.76 \ V)$

$\lim _{x \rightarrow 0} \frac{\tan x - \sin x}{x^3}$ is equal to

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$ (where $\rho_0$ is a constant and $r$ is measured from the centre). Consider two points $A$ and $B$ at distances $x$ and $y$ respectively from the centre,such that $x < R$ and $y > R$. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

The gold numbers of $A$,$B$,$C$,and $D$ are $0.04$,$0.002$,$10$,and $25$ respectively. The protective power of $A$,$B$,$C$,and $D$ are in the order: