Twelve cells each having the same e.m.f are connected in series and are kept to a closed box. Some of the cell are connected in reverse order .The battery is connected in series with an ammeter an external resistance `R` and two cells of the same type as an in the battery .The current when they and support each other is `3` ampere and current is `2` ampare when the two oppose each other. How many cells are connected in reverse order ?

Options

A. 4
B. 1
C. 3
D. 2

Answer

To solve the problem, we need to analyze the situation with the cells connected in series and how they affect the total electromotive force (e.m.f.) and current when some cells are reversed.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have 12 cells, each with the same e.m.f. (let's denote it as \( E \)).
- Some of these cells are connected in reverse order. Let \( n \) be the number of cells connected in reverse.

2. **Total e.m.f. Calculation**:
- When \( n \) cells are reversed, the effective e.m.f. of the battery can be calculated as:
\[ \text{Total e.m.f.} = 12E - nE - nE = (12 - 2n)E \]
- The two additional cells connected in series (which are not reversed) contribute an additional \( 2E \).
- Therefore, the effective e.m.f. when the two additional cells support the main battery is:
\[ \text{Total e.m.f. (supporting)} = (12 - 2n)E + 2E = (14 - 2n)E \]

3. **Current Calculation When Supporting**:
- According to Ohm's law, the current \( I_1 \) when the two additional cells support the battery is given by:
\[ I_1 = \frac{(14 - 2n)E}{R} \]
- We know from the problem statement that \( I_1 = 3 \) A, so we can write:
\[ \frac{(14 - 2n)E}{R} = 3 \quad \text{(1)} \]

4. **Current Calculation When Opposing**:
- When the two additional cells oppose the main battery, the effective e.m.f. becomes:
\[ \text{Total e.m.f. (opposing)} = (12 - 2n)E - 2E = (10 - 2n)E \]
- The current \( I_2 \) in this case is:
\[ I_2 = \frac{(10 - 2n)E}{R} \]
- From the problem statement, we know \( I_2 = 2 \) A, so we can write:
\[ \frac{(10 - 2n)E}{R} = 2 \quad \text{(2)} \]

5. **Setting Up the Equations**:
- From equations (1) and (2), we have:
\[ (14 - 2n)E = 3R \quad \text{(1)} \]
\[ (10 - 2n)E = 2R \quad \text{(2)} \]

6. **Dividing the Equations**:
- Dividing equation (1) by equation (2):
\[ \frac{(14 - 2n)E}{(10 - 2n)E} = \frac{3R}{2R} \]
- This simplifies to:
\[ \frac{14 - 2n}{10 - 2n} = \frac{3}{2} \]

7. **Cross Multiplying**:
- Cross multiplying gives:
\[ 2(14 - 2n) = 3(10 - 2n) \]
- Expanding both sides:
\[ 28 - 4n = 30 - 6n \]

8. **Solving for \( n \)**:
- Rearranging gives:
\[ 6n - 4n = 30 - 28 \]
\[ 2n = 2 \]
\[ n = 1 \]

9. **Conclusion**:
- The number of cells connected in reverse order is \( n = 1 \).

### Final Answer:
The number of cells connected in reverse order is **1**.