Ammonium dichromate on heating liberates a gas. The same gas
will be obtained by :

Options

A. heating `NaNO_(2)` and `NH_(4)Cl`.
B. treating `H_(2)O_(2)` "with" `NaNO_(2)`.
C. "passing ammonia gas over red hot" `CuO`.
D. None of these

Explanation

To solve the question regarding the gas liberated when ammonium dichromate is heated, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction of Ammonium Dichromate on Heating**:
- Ammonium dichromate \((NH_4)_2Cr_2O_7\) decomposes upon heating to produce nitrogen gas \((N_2)\), water \((H_2O)\), and chromium(III) oxide \((Cr_2O_3)\).
- The balanced equation for this reaction is:
\[ (NH_4)_2Cr_2O_7 \rightarrow N_2 + 4H_2O + Cr_2O_3 \]
- From this reaction, we conclude that the gas liberated is nitrogen gas \((N_2)\).

2. **Examine the Options for Gas Liberation**:
- We need to evaluate each option to see if it produces nitrogen gas \((N_2)\).

3. **Option 1: Reaction of \(NaNO_2\) with \(NH_4Cl\)**:
- The reaction can be represented as:
\[ NH_4Cl + NaNO_2 \rightarrow NH_4NO_2 + NaCl \]
- Ammonium nitrite \((NH_4NO_2)\) is unstable and decomposes upon heating:
\[ NH_4NO_2 \rightarrow N_2 + 2H_2O \]
- Therefore, this option produces nitrogen gas \((N_2)\).

4. **Option 2: Reaction of \(H_2O_2\) with \(NaNO_2\)**:
- The reaction is:
\[ H_2O_2 + NaNO_2 \rightarrow NaNO_3 + H_2O \]
- This reaction does not produce nitrogen gas \((N_2)\).

5. **Option 3: Passing Ammonia Gas over Hot Red \(CuO\)**:
- The reaction can be represented as:
\[ 2NH_3 + 3CuO \rightarrow 3Cu + 3H_2O + N_2 \]
- This reaction produces nitrogen gas \((N_2)\).

6. **Conclusion**:
- From the analysis, options 1 and 3 produce nitrogen gas \((N_2)\).
- Therefore, the correct answers are options 1 and 3.

### Final Answer:
The same gas (nitrogen gas, \(N_2\)) will be obtained by:
- Option 1: \(NaNO_2 + NH_4Cl\)
- Option 3: Passing ammonia gas over hot red \(CuO\)