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 such each other is `3` ampere and current is `2` ampare when the two oppose each other. How many cells are connected in servese order ?

Explanation

To solve the problem, we need to determine how many cells are connected in reverse order in a series of 12 cells, given the current readings when the cells are connected in different configurations. Let's follow the steps to find the solution.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( N = 12 \) (total number of cells).
- Let \( M \) be the number of cells connected in reverse order.
- Let \( E \) be the EMF of each cell.
- The total EMF of the battery when all cells are connected in series is given by \( E_{\text{net}} = (N - 2M)E \).

2. **Current When Cells Support Each Other:**
- When the two additional cells (connected in series) support the battery, the effective EMF is:
\[ E_{\text{net}} = (N - 2M)E + 2E = (N - 2M + 2)E \]
- The current \( I_1 \) when they support each other is given as \( 3 \, \text{A} \):
\[ I_1 = \frac{(N - 2M + 2)E}{R} = 3 \]

3. **Current When Cells Oppose Each Other:**
- When the two additional cells oppose the battery, the effective EMF is:
\[ E_{\text{net}} = (N - 2M)E - 2E = (N - 2M - 2)E \]
- The current \( I_2 \) when they oppose each other is given as \( 2 \, \text{A} \):
\[ I_2 = \frac{(N - 2M - 2)E}{R} = 2 \]

4. **Set Up the Equations:**
- From the first equation:
\[ (N - 2M + 2)E = 3R \quad \text{(1)} \]
- From the second equation:
\[ (N - 2M - 2)E = 2R \quad \text{(2)} \]

5. **Divide the Two Equations:**
- Dividing equation (1) by equation (2):
\[ \frac{(N - 2M + 2)E}{(N - 2M - 2)E} = \frac{3R}{2R} \]
- This simplifies to:
\[ \frac{N - 2M + 2}{N - 2M - 2} = \frac{3}{2} \]

6. **Cross Multiply:**
- Cross multiplying gives:
\[ 2(N - 2M + 2) = 3(N - 2M - 2) \]
- Expanding both sides:
\[ 2N - 4M + 4 = 3N - 6M - 6 \]

7. **Rearranging the Equation:**
- Rearranging gives:
\[ 2N + 10 = N + 2M \]
- Thus:
\[ N + 10 = 2M \]

8. **Substituting \( N = 12 \):**
- Substitute \( N \) into the equation:
\[ 12 + 10 = 2M \]
- Therefore:
\[ 22 = 2M \implies M = 11 \]

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

### Final Answer:
**1 cell is connected in reverse order.**