Two physical quantities P and Q have different dimensions. Which of the following mathematical operation is/are possible?

Options

A. `(P)/(Q)`
B. `PQ`
C. `P+Q`
D. `P-Q`

Explanation

To determine which mathematical operations are possible between two physical quantities P and Q that have different dimensions, we can analyze the operations one by one.

### Step-by-Step Solution:

1. **Understanding Dimensions**:
- Physical quantities have dimensions that define their physical nature. For example, mass (M), length (L), and time (T) are fundamental dimensions.

2. **Addition and Subtraction**:
- Addition and subtraction of physical quantities can only be performed if the quantities have the same dimensions.
- Since P and Q have different dimensions, we cannot add or subtract them.
- **Conclusion**: Addition and subtraction are **not possible**.

3. **Multiplication**:
- Multiplication of physical quantities is always possible, regardless of their dimensions.
- For example, if P has dimensions of mass (M) and Q has dimensions of length (L), then P * Q will have dimensions of ML.
- **Conclusion**: Multiplication is **possible**.

4. **Division**:
- Division of physical quantities is also always possible, regardless of their dimensions.
- For instance, if we divide P (with dimensions M) by Q (with dimensions L), the result will have dimensions of M/L.
- **Conclusion**: Division is **possible**.

### Final Conclusion:
- The operations that are possible between two physical quantities P and Q with different dimensions are:
- **Multiplication**
- **Division**
- The operations that are **not possible** are:
- **Addition**
- **Subtraction**

### Summary of Possible Operations:
- **Possible**: Multiplication, Division
- **Not Possible**: Addition, Subtraction