$A$ solution of concentration $C \ g \ \text{equiv}/L$ has a specific resistance $R$. The equivalent conductance of the solution is

In the extraction of aluminium:
Process $X$: applied for red bauxite to remove iron oxide (chief impurity).
Process $Y$: (Serpeck's process) applied for white bauxite to remove $Z$ (chief impurity). Then,process $X$ and impurity $Z$ are:

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is

If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,3)$,then the equation of the plane is

The solution of $\frac{dy}{dx} + 1 = e^{x+y}$ is

One mole of $N_2H_4$ loses $10$ moles of electrons to form a new compound $Z$. Assuming that all the nitrogen atoms appear in the new compound,what is the oxidation state of nitrogen in $Z$? (There is no change in the oxidation state of hydrogen.)