Aluminium is extracted from alumina $(Al_2O_3)$ by electrolysis of a molten mixture of:

The image formed by a concave mirror of focal length $6 \ cm$ is $3$ times the size of the object. The distance of the object from the mirror is......$cm$.

$A$ convex lens of focal length $0.15 \ m$ is made of a material of refractive index $\frac{3}{2}$. When it is placed in a liquid,its focal length increases by $0.225 \ m$. The refractive index of the liquid is

$Na^+$,$Mg^{2+}$,$Al^{3+}$,and $Si^{4+}$ are isoelectronic. What is the order of their ionic radii?

$A$ square of side $3\;cm$ is placed at a distance of $25\;cm$ from a concave mirror of focal length $10\;cm$. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is $......\;cm^2$.

An ink mark is made on a piece of paper on which a glass slab of thickness $t$ is placed. The ink mark appears to be raised up through a distance $x$ when viewed at nearly normal incidence. If the refractive index of the material of the glass slab is $\mu$,then the thickness of the glass slab is given by: