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(C) Let us analyze each option:$(A)$ $Mg_2C_3 + 4H_2O 	o 2Mg(OH)_2 + C_3H_4$ (Propyne); $Al_4C_3 + 12H_2O 	o 4Al(OH)_3 + 3CH_4$ (Methane). Gases are

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$NH_4Cl \xrightarrow{NaOH(aq.)} X$; $NaNO_3 \xrightarrow{Al/NaOH(aq.)} Y$

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(C) Let us analyze each option:$(A)$ $Mg_2C_3 + 4H_2O 	o 2Mg(OH)_2 + C_3H_4$ (Propyne); $Al_4C_3 + 12H_2O 	o 4Al(OH)_3 + 3CH_4$ (Methane). Gases are different.$(B)$ $NH_4NO_3 \xrightarrow{\Delta} N_2O + 2H_2O$; $(NH_4)_2Cr_2O_7 \xrightarrow{\Delta} N_2 + Cr_2O_3 + 4H_2O$. Gases are different.$(C)$ $NH_4Cl + NaOH 	o NaCl + H_2O + NH_3(X)$; $NaNO_3 + 8Al + 5NaOH + 18H_2O 	o 8Na[Al(OH)_4] + 3NH_3(Y)$. Both produce $NH_3$. Thus,$X = Y$.$(D)$ $3Cu + 8dil. HNO_3 	o 3Cu(NO_3)_2 + 4H_2O + 2NO(X)$; $3Ag + 4dil. HNO_3 	o 3AgNO_3 + 2H_2O + NO(Y)$. Both produce $NO$. Thus,$X = Y$.Note: In many competitive contexts,both $(C)$ and $(D)$ are considered correct as they produce the same gaseous products.

In which of the following options are the product gases $X$ and $Y$ (other than water vapour) the same?

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