Fill in the blanks:
$1.$ Heating lanthanoids with sulfur gives .......
$2.$ Mixed oxides of lanthanoids are used as catalysts in ..........

Mention the type of compounds formed when small atoms like $H$,$C$ and $N$ get trapped inside the crystal lattice of transition metals. Also,give the physical and chemical characteristics of these compounds.

Provide the structures for:
$1.$ $MnO_4^{-}$
$2.$ $MnO_4^{2-}$

The conversion of pig iron to steel frequently requires the addition of
$(I)$ oxygen or iron oxide
$(II)$ transition elements
$(III)$ inner transition elements
$(IV)$ silica

The colour of $K_2Cr_2O_7$ changes from red-orange to lemon-yellow on treatment with aqueous $KOH$ because of:

Given below are two statements:
Statement $I :$ Potassium permanganate on heating at $573 \ K$ forms potassium manganate.
Statement $II :$ Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in nature.
In the light of the above statements,choose the most appropriate answer from the options given below.