To solve this problem, we need to identify the products of the reaction catalyzed by nitrogenase in root nodules of leguminous plants.$\newline$Let's analyze the nitrogenase enzyme and its function:$\newline \bullet$Nitrogenase is an enzyme complex found in certain bacteria, including those in the root nodules of leguminous plants.$\newline \bullet$Its primary function is to catalyze the conversion of atmospheric nitrogen (N$_2$) into ammonia (NH$_3$).$\newline \bullet$The overall reaction catalyzed by nitrogenase can be represented as:$\newline$N$_2 + 8$H$^+ + 8$e$^- + 16$ATP$\rightarrow 2$NH$_3 +$H$_2 + 16$ADP$+ 16$P$_i \newline \bullet$From the reaction, it is clear that the products are ammonia (NH$_3$) and hydrogen gas (H$_2$).$\newline$Now, let's evaluate the given options:$\newline \bullet$Option 1: Nitrate alone - This is incorrect as nitrate is not a product of the nitrogenase reaction.$\newline \bullet$Option 2: Ammonia and oxygen - This is incorrect as oxygen is not a product of the nitrogenase reaction.$\newline \bullet$Option 3: Ammonia and hydrogen - This is correct as both ammonia and hydrogen are products of the nitrogenase reaction.$\newline \bullet$Option 4: Ammonia alone - This is incorrect as hydrogen is also a product of the reaction.$\newline$Therefore, the correct answer is Option 3: Ammonia and hydrogen.