Out of the following forces, the resultant of which cannot be `10N`?

Options

A. `15N` and `20N`
B. `10N` and `10N`
C. `5N` and `12N`
D. `12N` and `1N`

Explanation

To determine which set of forces cannot have a resultant of 10 Newtons, we need to analyze the possible resultant forces based on the given forces. The resultant force of two vectors (forces) can be calculated using the triangle law of vector addition, which states that the resultant lies between the difference and the sum of the two vectors.

### Step-by-Step Solution:

1. **Identify the Forces**: We have four pairs of forces to consider:
- Pair 1: 15 N and 20 N
- Pair 2: 10 N and 10 N
- Pair 3: 5 N and 12 N
- Pair 4: 12 N and 1 N

2. **Calculate the Resultant for Each Pair**:
- **Pair 1 (15 N and 20 N)**:
- Minimum resultant = |15 N - 20 N| = 5 N
- Maximum resultant = 15 N + 20 N = 35 N
- Possible resultant range: 5 N to 35 N (10 N is possible)

- **Pair 2 (10 N and 10 N)**:
- Minimum resultant = |10 N - 10 N| = 0 N
- Maximum resultant = 10 N + 10 N = 20 N
- Possible resultant range: 0 N to 20 N (10 N is possible)

- **Pair 3 (5 N and 12 N)**:
- Minimum resultant = |5 N - 12 N| = 7 N
- Maximum resultant = 5 N + 12 N = 17 N
- Possible resultant range: 7 N to 17 N (10 N is possible)

- **Pair 4 (12 N and 1 N)**:
- Minimum resultant = |12 N - 1 N| = 11 N
- Maximum resultant = 12 N + 1 N = 13 N
- Possible resultant range: 11 N to 13 N (10 N is NOT possible)

3. **Conclusion**: The only pair of forces for which the resultant cannot be 10 N is the fourth pair (12 N and 1 N).

### Final Answer:
The resultant of the forces 12 N and 1 N cannot be 10 N.