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On heating ammonium dichromate and barium azide separately we get:
A)N$_2$ in both cases.
B) N$_2$ with ammonium dichromate and NO with barium azide.
C) N$_2$O with ammonium dichromate and N$_2$ with barium azide.
D) N$_2$O with ammonium dichromate and NO$_2$ with barium azide.

Answer
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Hint: The heating of ammonium dichromate, and barium azide individually represents the decomposition reaction. Write down the chemical reactions for both the compounds. One product formed has very high dissociation energy and has a maximum percentage in earth’s atmosphere and the other one is the oxide of the previous non-metal.

Complete answer:
->First, let us discuss the chemical reaction on heating the ammonium dichromate. It produces chromium oxide, nitrogen gas, and water vapours on decomposition. The chromium oxide shows +3 oxidation state.
->The chemical reaction is
(NH$_4$)$_2$Cr$_2$O$_7$ (s) $\rightarrow$ Cr$_2$O$_3$ (s) + N$_2$ (g) + 4H$_2$O (g)

These impurities that are produced along-with nitrogen are removed by the thermal decomposition of ammonium dichromate. Another method which could be used in place of this is to pass these gaseous mixtures through sulfuric holding potassium dichromate.

->The second is heating of barium azide. It produces metallic barium, and a nitrogen gas.
->The chemical reaction is
          Ba(N$_3$)$_2$ $\rightarrow$ Ba + 3N$_2$
->Barium azides is also used in the preparation of azides of magnesium, lithium, potassium when it is reacted with their respective sulphates.
->As mentioned above the chemical reaction of ammonium dichromate, and barium azide separately, it can be concluded that N$_2$ gas is evolved in both the cases.

Hence the correct option is A.

Additional information:
The heating of barium azide is considered to be a source for obtaining the pure nitrogen, and it is explosive in nature. But if we talk about the ammonium dichromate, its reaction is based on ammonium dichromate volcano, it means on heating it looks like a miniature volcano.

Note:As mentioned chromium shows +3 oxidation state in chromium oxide (Cr$_2$O$_3$), here it will be 2x-6 = 0; it means -6 represents the charge of 3 oxygen atoms, i.e. -2 each, and for chromium consider the charge to be x, and it is neutral molecule, so it is equal to zero. Thus, we can calculate the oxidation state of chromium. The value of x attained i.e. 3 is the corresponding oxidation state.