Which of the following ores is used for the production of $K_2Cr_2O_7$?

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

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

Which of the following is a highly corrosive salt?

$I$. $4FeCr_2O_4 + 16NaOH + 7O_2 \rightarrow 8Na_2CrO_4 + 2Fe_2O_3 + 8H_2O$ (where $A = Na_2CrO_4$)
$II$. $2Na_2CrO_4 + H_2SO_4 \rightarrow Na_2Cr_2O_7 + Na_2SO_4 + H_2O$ (where $B = H_2SO_4$)
Compounds $(A)$ and $(B)$ are :

$KMnO_4$ decomposes on heating at $513 \ K$ to form $O_2$ along with