To solve this problem, we need to understand the reactions that occur in a blast furnace during the extraction of iron.$\\$In a blast furnace, the following reactions typically occur between 900 K and 1500 K:$\\$• Reduction of iron oxides:$\\$1. $$Fe$_2$O$_3 + 3$CO$\to 2$Fe$+ 3$CO$_2 \\$2. $$FeO$+$CO$\to$Fe$+$CO$_2 \\$• Formation of carbon monoxide:$\\$3. $$C$+$CO$_2 \to 2$CO$\\$• Formation of slag:$\\$4. $$CaO$+$SiO$_2 \to$CaSiO$_3 \\$Now, let's analyze each option:$\\$Option 1: $$Fe$_2$O$_3 +$CO$\to 2$FeO$+$CO$_2 \\$• This reaction is not typical in the blast furnace as it suggests the conversion of $$Fe$_2$O$_3$ to $$FeO$, \\$ which is not a reduction to metallic iron. Instead, $$Fe$_2$O$_3$ is directly reduced to iron.$\\$Option 2: $$FeO$+$CO$\to$Fe$+$CO$_2 \\$• This is a common reduction reaction in the blast furnace where iron(II) oxide is reduced to iron.$\\$Option 3: $$C$+$CO$_2 \to 2$CO$\\$• This reaction is known as the Boudouard reaction and is important for generating carbon monoxide,$\\$ which acts as a reducing agent in the furnace.$\\$Option 4: $$CaO$+$SiO$_2 \to$CaSiO$_3 \\$• This reaction forms slag, which is essential for removing impurities from the iron.$\\$Therefore, the reaction that does NOT take place in a blast furnace between 900 K to 1500 K is:$\\$Option 1: $$Fe$_2$O$_3 +$CO$\to 2$FeO$+$CO$_2 \\$This corresponds to the correct option.