`SO_(2)` and `CO_(2)` both turn lime water `(X)` milky, `SO_(2)` also turns `K_(2)Cr_(2)O_(7)//H^(+) (Y)` green while `O_(2)` is soluble in pyrogallol `(Z)` turning it black. These gases are to be detected in order by using these reagents. The order is:

Options

A. (X),(Y),(Z)
B. (Y),(X),(Z)
C. (X),(Z),(Y)
D. The correct order cannot be predicted.

Explanation

To determine the order of detection for the gases \( SO_2 \), \( CO_2 \), and \( O_2 \) using the given reagents, we will analyze the reactions step by step.

### Step 1: Detecting \( SO_2 \) using \( K_2Cr_2O_7/H^+ \) (Y)
- **Reaction**: \( SO_2 \) reacts with \( K_2Cr_2O_7 \) in an acidic medium. The \( Cr_2O_7^{2-} \) ions are reduced to \( Cr^{3+} \), which gives a green color.
- **Chemical Equation**:
\[ 3 SO_2 + 2 Cr_2O_7^{2-} + 8 H^+ \rightarrow 2 Cr^{3+} + 3 SO_4^{2-} + 4 H_2O \]
- **Conclusion**: Since \( SO_2 \) reacts and changes the color of the solution to green, it is detected first.

### Step 2: Detecting \( CO_2 \) using Lime Water (X)
- **Reaction**: \( CO_2 \) reacts with lime water (calcium hydroxide solution) to form calcium carbonate, which is a white precipitate.
- **Chemical Equation**:
\[ CO_2 + Ca(OH)_2 \rightarrow CaCO_3 \downarrow + H_2O \]
- **Conclusion**: The formation of a white precipitate indicates the presence of \( CO_2 \). Thus, it is detected second.

### Step 3: Detecting \( O_2 \) using Pyrogallol (Z)
- **Reaction**: \( O_2 \) dissolves in pyrogallol, leading to a color change (turning it black due to the formation of a complex).
- **Conclusion**: Since \( O_2 \) does not react with the previous reagents, it is detected last.

### Final Order of Detection
Based on the above reactions, the order of detection of the gases is:
1. \( SO_2 \) (using \( K_2Cr_2O_7/H^+ \) - Y)
2. \( CO_2 \) (using Lime Water - X)
3. \( O_2 \) (using Pyrogallol - Z)

Thus, the answer is **Y, X, Z**.