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

Options

A. (A),(B) ,(C )
B. (B),(C) ,(A)
C. (B),(A) ,(C )
D. (A),(C) ,(B)

Answer

To determine the order in which the gases \( SO_2 \), \( CO_2 \), and \( O_2 \) can be detected using the reagents lime water (A), \( K_2Cr_2O_7/H^+ \) (B), and pyrogallol (C), we can analyze the reactions of each gas with the respective reagents.

### Step-by-Step Solution:

1. **Identify the Reactions:**
- **Lime Water (A):** Both \( SO_2 \) and \( CO_2 \) turn lime water milky due to the formation of calcium carbonate.
- **\( K_2Cr_2O_7/H^+ \) (B):** \( SO_2 \) reduces \( K_2Cr_2O_7 \) in acidic medium, turning it from orange to green.
- **Pyrogallol (C):** \( O_2 \) reacts with pyrogallol, resulting in a color change to black due to the formation of a complex.

2. **Determine the Order of Detection:**
- First, we should detect \( SO_2 \) using reagent B. Since \( SO_2 \) can reduce \( K_2Cr_2O_7 \), it will be absorbed first, and thus removed from the mixture.
- Next, we can detect \( CO_2 \) using lime water (A). After \( SO_2 \) has been removed, \( CO_2 \) will react with lime water, turning it milky.
- Finally, we can detect \( O_2 \) using pyrogallol (C). After both \( SO_2 \) and \( CO_2 \) have been removed, \( O_2 \) will react with pyrogallol, turning it black.

3. **Final Order of Detection:**
- The order of detection is: **B (for \( SO_2 \)), A (for \( CO_2 \)), C (for \( O_2 \))**.

### Conclusion:
The correct order for detecting the gases is **B, A, C**.