Which of the following is true for the gaseous state?

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

In the following reaction,$A$ and $B$ respectively are:
$A$ $\xrightarrow{HBr} C_2H_5Br$ $\xrightarrow{B} A$

The first operation involved in a Carnot cycle is

The work function of a certain metal is $3.31 \times 10^{-19} \, J$. The maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength $5000 \, \text{Å}$ is: (Given: $h = 6.62 \times 10^{-34} \, J \cdot s$, $c = 3 \times 10^8 \, m/s$, $e = 1.6 \times 10^{-19} \, C$) (in $\text{eV}$)

The principal section of a glass prism is an isosceles triangle $ABC$ with $AB=AC$. The face $AC$ is silvered. $A$ ray of light is incident normally on the face $AB$ and after two reflections,it emerges from the base $BC$ perpendicular to the base. Angle $BAC$ of the prism is (in $^{\circ}$)