High purity copper metal is obtained by

$\int \left( \frac{2 - \sin 2x}{1 - \cos 2x} \right) e^x \, dx$ is equal to

Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively.
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$
$2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$
The equilibrium constants are related as

Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength $\lambda_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{\lambda_1}{2}$. The power radiated at $T_2$ is (in $P$)

What is the small,circular $DNA$ molecule present in a bacterial cell,in addition to the main genomic $DNA$,called?

$A$ photon of energy $E$ ejects a photoelectron from a metal surface whose work function is $W_0.$ If this electron enters into a uniform magnetic field of induction $B$ in a direction perpendicular to the field and describes a circular path of radius $r,$ then the radius $r$ is given by (in the usual notation):