The modern method of steel manufacturing is

Choose the correct option with reference to the following statements:
$(1)$ Pig iron is produced at a temperature of $1270 \ K$.
$(2)$ Pig iron contains $4 \%$ carbon.
$(3)$ Pig iron cannot be cast into a variety of shapes.
$(4)$ Pig iron contains small amounts of impurities like $P, S, Si, Mn$.

Which of the following statements is not correct?
$1$. Reduction of alumina to give aluminium by magnesium is thermodynamically feasible.
$2$. The point of intersection of $Al_2O_3$ and $MgO$ curves in Ellingham diagram is below $1665 \ K$.
$3$. Use of magnesium as reducing agent in metallurgy of aluminium is economical.
$4$. Ellingham diagram represents the graphical plot of Gibbs energy vs temperature for the formation of the oxides of common metals and reducing agents.

What is the role of limestone during the extraction of iron from haematite ore?

In the extraction of aluminium,bauxite $(Al_2O_3 \cdot 2H_2O)$ is dissolved in molten cryolite $(Na_3AlF_6)$ because:

In a blast furnace,iron oxide is reduced by: