1. We need compounds that give $N_2$ on heating below $300^ \circ\text{C}$.
   Since this is MCQM, we check each option independently.

2. Option A: $NH_4NO_3$ (ammonium nitrate)

On heating moderately, ammonium nitrate decomposes mainly as: $NH_4NO_3 \xrightarrow{\Delta} N_2O + 2H_2O$

It gives nitrous oxide $N_2O$, not $N_2$.

So, A is incorrect.

3. Option B: $(NH_4)_2Cr_2O_7$ (ammonium dichromate)

This is the well-known volcano reaction: $(NH_4)_2Cr_2O_7 \xrightarrow{\Delta} Cr_2O_3 + N_2 + 4H_2O$

Here, $N_2$ gas is produced.

This decomposition occurs well below $300^\circ\text{C}$.

So, B is correct.

4. Option C: $Ba(N_3)_2$ (barium azide)

Metal azides decompose on heating to give the metal and nitrogen gas: $Ba(N_3)_2 \xrightarrow{\Delta} Ba + 3N_2$

Hence, $N_2$ is produced.

Azides generally decompose below about $300^\circ\text{C}$.

So, C is correct.

5. Option D: $Mg_3N_2$ (magnesium nitride)

Magnesium nitride does not give $N_2$ on thermal decomposition below $300^\circ\text{C}$. Instead, nitrides are generally stable ionic compounds. They react with water as: $Mg_3N_2 + 6H_2O \rightarrow 3Mg(OH)_2 + 2NH_3$

Thus it does not thermally decompose to give $N_2$ under the stated condition.

So, D is incorrect.

6. Final answer

The compounds which generate $N_2$ gas upon thermal decomposition below $300^\circ\text{C}$ are: $\boxed{B,\ C}$

7. Comparison with stored correct answer

Stored correct answer: B, C
Derived answer: B, C

So, the derived answer agrees with the stored answer.